Model Analysis
Nikhil Gupta
2019-02-11 18:56:55
sessionInfo()## R version 3.5.1 (2018-07-02)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 17134)
##
## Matrix products: default
##
## locale:
## [1] LC_COLLATE=English_United States.1252
## [2] LC_CTYPE=English_United States.1252
## [3] LC_MONETARY=English_United States.1252
## [4] LC_NUMERIC=C
## [5] LC_TIME=English_United States.1252
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## loaded via a namespace (and not attached):
## [1] compiler_3.5.1 magrittr_1.5 tools_3.5.1 htmltools_0.3.6
## [5] yaml_2.2.0 Rcpp_1.0.0 stringi_1.2.4 rmarkdown_1.11
## [9] knitr_1.20 stringr_1.3.1 digest_0.6.18 evaluate_0.12User Inputs
output.var = params$output.var
transform.abs = params$transform.abs
log.pred = params$log.pred
eda = params$eda
algo.forward = params$algo.forward
algo.backward = params$algo.backward
algo.stepwise = params$algo.stepwise
algo.LASSO = params$algo.LASSO
algo.LARS = params$algo.LARS
algo.forward.caret = params$algo.forward.caret
algo.backward.caret = params$algo.backward.caret
algo.stepwise.caret = params$algo.stepwise.caret
algo.LASSO.caret = params$algo.LASSO.caret
algo.LARS.caret = params$algo.LARS.caret
message("Parameters used for training/prediction: ")## Parameters used for training/prediction:str(params)## List of 14
## $ output.var : chr "y3"
## $ transform.abs : logi FALSE
## $ log.pred : logi FALSE
## $ eda : logi FALSE
## $ algo.forward : logi FALSE
## $ algo.backward : logi FALSE
## $ algo.stepwise : logi FALSE
## $ algo.LASSO : logi FALSE
## $ algo.LARS : logi FALSE
## $ algo.forward.caret : logi TRUE
## $ algo.backward.caret: logi TRUE
## $ algo.stepwise.caret: logi TRUE
## $ algo.LASSO.caret : logi TRUE
## $ algo.LARS.caret : logi TRUE# Setup Labels
# alt.scale.label.name = Alternate Scale variable name
# - if predicting on log, then alt.scale is normal scale
# - if predicting on normal scale, then alt.scale is log scale
if (log.pred == TRUE){
label.names = paste('log.',output.var,sep="")
alt.scale.label.name = output.var
}
if (log.pred == FALSE){
label.names = output.var
alt.scale.label.name = paste('log.',output.var,sep="")
}Prepare Data
Read and Clean Features
features = read.csv("../../Data/features.csv")
features.highprec = read.csv("../../Data/features_highprec.csv")all.equal(features, features.highprec)## [1] "Component \"x11\": Mean relative difference: 0.001401482"
## [2] "Component \"stat9\": Mean relative difference: 0.0002946299"
## [3] "Component \"stat12\": Mean relative difference: 0.0005151515"
## [4] "Component \"stat13\": Mean relative difference: 0.001354369"
## [5] "Component \"stat18\": Mean relative difference: 0.0005141104"
## [6] "Component \"stat22\": Mean relative difference: 0.001135977"
## [7] "Component \"stat25\": Mean relative difference: 0.0001884615"
## [8] "Component \"stat29\": Mean relative difference: 0.001083691"
## [9] "Component \"stat36\": Mean relative difference: 0.00021513"
## [10] "Component \"stat37\": Mean relative difference: 0.0004578125"
## [11] "Component \"stat43\": Mean relative difference: 0.0003473684"
## [12] "Component \"stat45\": Mean relative difference: 0.0002951699"
## [13] "Component \"stat46\": Mean relative difference: 0.0009745763"
## [14] "Component \"stat47\": Mean relative difference: 8.829902e-05"
## [15] "Component \"stat55\": Mean relative difference: 0.001438066"
## [16] "Component \"stat57\": Mean relative difference: 0.0001056911"
## [17] "Component \"stat58\": Mean relative difference: 0.0004882261"
## [18] "Component \"stat60\": Mean relative difference: 0.0002408377"
## [19] "Component \"stat62\": Mean relative difference: 0.0004885106"
## [20] "Component \"stat66\": Mean relative difference: 1.73913e-06"
## [21] "Component \"stat67\": Mean relative difference: 0.0006265823"
## [22] "Component \"stat73\": Mean relative difference: 0.003846154"
## [23] "Component \"stat75\": Mean relative difference: 0.002334906"
## [24] "Component \"stat83\": Mean relative difference: 0.0005628415"
## [25] "Component \"stat86\": Mean relative difference: 0.0006104418"
## [26] "Component \"stat94\": Mean relative difference: 0.001005115"
## [27] "Component \"stat97\": Mean relative difference: 0.0003551913"
## [28] "Component \"stat98\": Mean relative difference: 0.0006157635"
## [29] "Component \"stat106\": Mean relative difference: 0.0008267717"
## [30] "Component \"stat109\": Mean relative difference: 0.0005121359"
## [31] "Component \"stat110\": Mean relative difference: 0.0007615527"
## [32] "Component \"stat111\": Mean relative difference: 0.001336134"
## [33] "Component \"stat114\": Mean relative difference: 7.680492e-05"
## [34] "Component \"stat117\": Mean relative difference: 0.0002421784"
## [35] "Component \"stat122\": Mean relative difference: 0.0006521084"
## [36] "Component \"stat123\": Mean relative difference: 8.333333e-05"
## [37] "Component \"stat125\": Mean relative difference: 0.002385135"
## [38] "Component \"stat130\": Mean relative difference: 0.001874016"
## [39] "Component \"stat132\": Mean relative difference: 0.0003193182"
## [40] "Component \"stat135\": Mean relative difference: 0.0001622517"
## [41] "Component \"stat136\": Mean relative difference: 7.722008e-05"
## [42] "Component \"stat138\": Mean relative difference: 0.0009739953"
## [43] "Component \"stat143\": Mean relative difference: 0.0004845361"
## [44] "Component \"stat146\": Mean relative difference: 0.0005821596"
## [45] "Component \"stat148\": Mean relative difference: 0.0005366922"
## [46] "Component \"stat153\": Mean relative difference: 0.0001557522"
## [47] "Component \"stat154\": Mean relative difference: 0.001351916"
## [48] "Component \"stat157\": Mean relative difference: 0.0005427928"
## [49] "Component \"stat162\": Mean relative difference: 0.002622951"
## [50] "Component \"stat167\": Mean relative difference: 0.0005905172"
## [51] "Component \"stat168\": Mean relative difference: 0.0002791096"
## [52] "Component \"stat169\": Mean relative difference: 0.0004121827"
## [53] "Component \"stat170\": Mean relative difference: 0.0004705882"
## [54] "Component \"stat174\": Mean relative difference: 0.0003822894"
## [55] "Component \"stat179\": Mean relative difference: 0.0008286604"
## [56] "Component \"stat184\": Mean relative difference: 0.0007526718"
## [57] "Component \"stat187\": Mean relative difference: 0.0005122768"
## [58] "Component \"stat193\": Mean relative difference: 4.215116e-05"
## [59] "Component \"stat199\": Mean relative difference: 0.002155844"
## [60] "Component \"stat203\": Mean relative difference: 0.0003738318"
## [61] "Component \"stat213\": Mean relative difference: 0.000667676"
## [62] "Component \"stat215\": Mean relative difference: 0.0003997955"head(features)## JobName x1 x2 x3 x4 x5 x6
## 1 Job_00001 2.0734508 4.917267 19.96188 3.520878 7.861051 1.6067589
## 2 Job_00002 2.2682543 4.955773 19.11939 19.763031 6.931355 1.3622041
## 3 Job_00003 1.7424456 2.059819 13.37912 38.829132 6.274053 2.0529845
## 4 Job_00004 0.7873555 2.613983 17.23044 64.402557 5.377652 0.9067419
## 5 Job_00005 2.3342753 4.299076 14.64883 52.537304 6.793368 2.4605792
## 6 Job_00006 1.2365089 2.795370 11.13127 96.819939 6.583971 2.3510606
## x7 x8 x9 x10 x11 x12 x13
## 1 2.979479 8.537228 1.103368 4.6089458 1.05e-07 7.995825 13.215498
## 2 2.388119 6.561461 0.588572 1.0283282 1.03e-07 7.486966 22.557224
## 3 2.043592 10.275595 4.834385 4.3872848 1.06e-07 6.350142 15.049810
## 4 2.395118 13.487331 3.340190 4.5053501 9.47e-08 9.548698 17.170635
## 5 2.891535 9.362389 1.246039 1.7333300 1.01e-07 9.596095 5.794567
## 6 1.247838 7.033354 1.852231 0.4839371 1.07e-07 3.810983 23.863169
## x14 x15 x16 x17 x18 x19 x20
## 1 4.377983 0.2370623 6.075459 3.988347 4.767475 2.698775 1.035893
## 2 2.059315 0.5638121 6.903891 4.152054 6.849232 9.620731 1.915288
## 3 3.260057 2.0603445 8.424065 4.489893 3.493591 4.715386 1.558103
## 4 3.093478 1.8806034 11.189792 2.134271 5.588357 5.107871 1.489588
## 5 3.943076 1.5820830 7.096742 3.563378 7.765610 1.360272 1.240283
## 6 1.280562 1.1733382 7.062051 1.341864 7.748325 5.009365 1.725179
## x21 x22 x23 stat1 stat2 stat3 stat4
## 1 42.36548 1.356213 2.699796 2.3801832 0.1883335 -1.2284011 -0.5999233
## 2 26.63295 4.053961 2.375127 -1.4069480 1.8140973 1.6204884 2.6422672
## 3 20.09693 3.079888 4.488420 -0.7672566 -0.1230289 1.1415752 2.9805934
## 4 32.60415 1.355396 3.402398 0.4371202 -1.9355906 0.9028624 -1.6025400
## 5 44.58361 1.940301 2.249011 2.4492466 -0.6172000 -2.5520642 -2.1485929
## 6 28.75102 2.500499 5.563972 -1.7899084 1.8853619 2.4154840 -2.6022179
## stat5 stat6 stat7 stat8 stat9 stat10
## 1 0.148893163 -0.6622978 -2.4851868 0.3647782 2.5364335 2.92067981
## 2 1.920768980 1.7411555 -1.9599979 -2.0190558 -1.3732762 -0.31642506
## 3 2.422584300 -0.4166040 2.2205689 -2.6741531 0.4844292 2.73379230
## 4 -0.001795933 -0.6946563 -0.3693534 -0.9709467 1.7960306 0.74771154
## 5 -2.311132430 -1.0166832 2.7269876 1.5424492 -1.3156369 -0.09767897
## 6 -1.785491470 -1.8599915 1.4875095 2.0188572 -1.4892503 -1.41103566
## stat11 stat12 stat13 stat14 stat15 stat16
## 1 -2.3228905 -2.480567 -0.6335157 -0.3650149 -0.5322812 0.6029300
## 2 -0.8547903 1.119316 0.7227427 0.2121097 -0.1452281 -2.0361528
## 3 -2.1821580 2.865401 -2.9756081 2.9871745 1.9539525 -1.8857163
## 4 1.3982378 1.856765 -1.0379983 2.3341896 2.3057184 -2.8947697
## 5 0.9567220 2.567549 0.3184886 1.0307668 0.1644241 -0.6613821
## 6 0.5341771 -1.461822 0.4402476 -1.9282095 -0.3680157 1.8188807
## stat17 stat18 stat19 stat20 stat21 stat22
## 1 -1.04516208 2.3544915 2.4049001 0.2633883 -0.9788178 1.7868229
## 2 0.09513074 0.4727738 1.8899702 2.7892542 -1.3919091 -1.7198164
## 3 0.40285346 1.4655282 -1.4952788 2.9162340 -2.3893208 2.8161423
## 4 2.97446084 2.3896182 2.3083484 -1.1894441 -2.1982553 1.3666242
## 5 -0.98465055 0.6900643 1.5894209 -2.1204538 1.7961155 -0.9362189
## 6 -1.45726359 -2.1139548 -0.3964904 1.1764175 -2.9100556 -2.1359294
## stat23 stat24 stat25 stat26 stat27 stat28
## 1 -2.3718851 2.8580718 -0.4719713 -2.817086 -0.9518474 2.88892484
## 2 -2.3293245 1.5577759 -1.9569720 1.554194 -0.5081459 -1.58715141
## 3 -2.5402296 0.1422861 0.3572798 -1.051886 -2.1541717 0.03074004
## 4 -1.9679050 -1.4077642 2.5097435 1.683121 -0.2549745 -2.90384054
## 5 2.0523429 -2.2084844 -1.9280857 -2.116736 1.8180779 -1.42167580
## 6 0.2184991 -0.7599817 2.6880329 -2.903350 -1.0733233 -2.92416644
## stat29 stat30 stat31 stat32 stat33 stat34
## 1 0.7991088 -2.0059092 -0.2461502 0.6482101 -2.87462163 -0.3601543
## 2 1.9758110 -0.3874187 1.3566630 2.6493473 2.28463054 1.8591728
## 3 -0.4460218 1.0279679 1.3998452 -1.0183365 1.41109037 -2.4183984
## 4 1.0571996 2.5588036 -2.9830337 -1.1299983 0.05470414 -1.5566561
## 5 0.8854889 2.2774174 2.6499031 2.3053405 -2.39148426 -1.8272992
## 6 -0.8405267 0.1311945 0.4321289 -2.9622040 -2.55387473 2.6396458
## stat35 stat36 stat37 stat38 stat39 stat40
## 1 2.4286051 -0.5420244 -2.6782637 -2.8874269 -0.8945006 1.1749642
## 2 1.3709245 -1.3714181 1.3901204 1.2273489 -0.8934880 1.0540369
## 3 -0.9805572 2.0571353 0.8845031 2.0574493 1.1222047 1.8528618
## 4 1.0969149 -2.2820673 1.8852408 0.5391517 2.7334342 -0.4372566
## 5 -1.0971669 1.4867796 -2.3738465 -0.3743561 1.4266498 1.2551680
## 6 0.4584349 -2.2696617 -0.9935142 -0.5350499 -0.7874799 2.0009417
## stat41 stat42 stat43 stat44 stat45 stat46
## 1 -1.0474428 -1.3909023 2.54110503 -1.4320793 0.6298335 -2.09296608
## 2 2.5380247 1.6476108 0.44128850 -2.5049477 1.2726039 1.72492969
## 3 1.1477574 0.2288794 0.08891252 2.3044751 -0.7735722 -0.07302936
## 4 -1.3808300 -2.7900956 2.38297582 0.1686397 -2.1591296 1.60828602
## 5 0.2257536 1.9542116 2.66429019 0.8026123 -1.5521187 1.61751962
## 6 -1.3364114 -2.2898803 2.80735397 -0.8413086 1.0057797 -1.50653386
## stat47 stat48 stat49 stat50 stat51 stat52
## 1 -2.8318939 2.1445766 0.5668035 0.1544579 0.6291955 2.2197027
## 2 -0.5804687 -1.3689737 1.4908396 1.2465997 0.8896304 -2.6024318
## 3 0.7918019 1.5712964 1.1038082 -0.2545658 -2.1662638 0.2660159
## 4 -1.8894132 0.5680230 -0.7023218 -0.3972188 0.1578027 2.1770194
## 5 2.1088455 -2.7195437 2.1961412 -0.2615084 1.2109556 0.8260623
## 6 -1.4400891 -0.9421459 -1.7324599 -2.1720727 -2.8129435 0.6958785
## stat53 stat54 stat55 stat56 stat57 stat58
## 1 2.176805 0.5546907 -2.19704103 -0.2884173 1.3232913 -1.32824039
## 2 -2.107441 1.3864788 0.08781975 1.9998228 0.8014438 -0.26979154
## 3 1.234197 2.1337581 1.65231645 -0.4388691 -0.1811156 2.11277962
## 4 2.535406 -2.1387620 0.12856023 -1.9906180 0.9626449 1.65232646
## 5 -2.457080 2.1633499 0.60441124 2.5449364 -1.4978440 2.60542655
## 6 2.003033 -0.5379940 -2.19647264 -1.1954677 -0.5974466 -0.04703835
## stat59 stat60 stat61 stat62 stat63 stat64
## 1 1.24239659 -2.5798278 1.327928 1.68560362 0.6284891 -1.6798652
## 2 0.06379301 0.9465770 1.116928 0.03128772 -2.1944375 0.3382609
## 3 0.93223447 2.4597080 0.465251 -1.71033382 -0.5156728 1.8276784
## 4 -0.29840910 0.7273473 -2.313066 -1.47696018 2.5910559 -1.5127999
## 5 -1.17610002 -1.7948418 -2.669305 0.17813617 2.8956099 2.9411416
## 6 -1.01793981 0.2817057 2.228023 -0.86494124 -0.9747949 -0.1569053
## stat65 stat66 stat67 stat68 stat69 stat70
## 1 -2.9490898 -0.3325469 1.5745990 -2.2978280 1.5451891 -1.345990
## 2 -1.1174885 -1.5728682 -2.9229002 0.2658547 -1.9616533 2.506130
## 3 -0.2231264 -0.4503301 0.7932286 -1.2453773 -2.2309763 2.309761
## 4 -0.3522418 -2.0720532 0.9442933 2.9212906 0.5100371 -2.441108
## 5 -2.1648991 1.2002029 2.8266985 0.7461294 1.6772674 -1.280000
## 6 -2.2295458 1.1446493 0.2024925 -0.2983998 -2.8203752 1.224030
## stat71 stat72 stat73 stat74 stat75 stat76
## 1 1.0260956 2.1071210 2.6625669 -2.8924677 -0.02132523 -2.5058765
## 2 0.3525076 1.6922342 -1.2167022 -1.7271879 2.21176434 1.9329683
## 3 -2.1799035 -2.2645276 0.1415582 0.9887453 1.95592320 0.2951785
## 4 -2.4051409 2.0876484 -0.8632146 0.4011389 -1.16986716 -1.2391174
## 5 1.3538754 -0.8089395 -0.5122626 -2.1696892 1.07344925 2.6696169
## 6 -2.8073371 -1.4450488 0.5481212 -1.4381690 0.80917043 -0.1365944
## stat77 stat78 stat79 stat80 stat81 stat82
## 1 -2.5631845 -2.40331340 0.38416120 -1.2564875 -0.1550840 -1.1762617
## 2 -0.4462085 0.38400793 1.80483031 -0.8387642 0.7624431 0.9936900
## 3 1.6757870 -1.81900752 2.70904708 -0.3201959 2.5754235 1.6346260
## 4 -2.1012006 -2.24691081 1.78056848 1.0323739 1.0762523 2.1343851
## 5 -2.5736733 -1.99958372 -0.05388495 -2.5630073 -2.8783002 -0.5752426
## 6 1.6143972 0.03233746 2.90835762 1.4000487 2.9275615 -2.8503830
## stat83 stat84 stat85 stat86 stat87 stat88
## 1 1.2840565 -2.6794965 1.3956039 -1.5290235 2.221152 2.3794982
## 2 -0.2380048 1.9314318 -1.6747955 -0.3663656 1.582659 -0.5222489
## 3 -0.9150769 -1.5520337 2.4186287 2.7273662 1.306642 0.1320062
## 4 -2.5824408 -2.7775943 0.5085060 0.4689015 2.053348 0.7957955
## 5 -1.0017741 -0.2009138 0.3770109 2.4335201 -1.118058 1.3953410
## 6 2.4891765 2.9931953 -1.4171852 0.3905659 -1.856119 -2.1690490
## stat89 stat90 stat91 stat92 stat93 stat94
## 1 -0.9885110 -0.8873261 -2.7810929 -1.53325891 2.6002395 1.8890998
## 2 0.9982028 -1.2382015 -0.1574496 0.41086048 -0.5412626 -0.2421387
## 3 0.5956759 1.6871066 2.2452753 2.74279594 -1.5860478 2.9393122
## 4 2.0902634 2.1752586 -2.0677712 -2.37861037 1.1653302 0.1500632
## 5 2.9820614 0.8111660 -0.7842287 0.03766387 -1.1681970 2.1217251
## 6 -1.7428021 0.1579032 1.7456742 -0.36858466 -0.1304616 -1.4555819
## stat95 stat96 stat97 stat98 stat99 stat100
## 1 -2.6056035 -0.5814857 2.57652426 -2.3297751 2.6324007 1.445827
## 2 -2.0271583 -0.9126074 2.49582648 0.9745382 1.1339203 -2.549544
## 3 0.3823181 -0.6324139 2.46221566 1.1151560 0.4624891 0.107072
## 4 2.6414623 -0.6630505 2.10394859 1.2627635 0.4861740 1.697012
## 5 1.4642254 2.6485956 -0.07699547 0.6219473 -1.8815142 -2.685463
## 6 1.8937331 -0.4690555 1.04671776 -0.5879866 -0.9766789 2.405940
## stat101 stat102 stat103 stat104 stat105 stat106
## 1 -2.1158021 2.603936 1.7745128 -1.8903574 -1.8558655 1.0122044
## 2 -2.7998588 -2.267895 0.5336456 -0.2859477 -0.5196246 -0.9417582
## 3 0.7969509 -1.744906 -0.7960327 1.9767258 -0.2007264 -0.7872376
## 4 1.7071959 -1.540221 1.6770362 1.5395796 -0.4855365 -1.2894115
## 5 -1.4627420 -1.700983 2.4376490 0.2731541 1.5275587 1.3256483
## 6 2.6888530 1.090155 2.0769854 1.9615480 1.8689761 2.8975825
## stat107 stat108 stat109 stat110 stat111 stat112
## 1 1.954508 -0.3376471 2.503084 0.3099165 2.7209847 -2.3911204
## 2 -2.515160 0.3998704 -1.077093 2.4228268 -0.7759693 0.2513882
## 3 1.888827 1.5819857 -2.066659 -2.0008364 0.6997684 2.6157095
## 4 1.076395 -1.8524148 -2.689204 1.0985872 1.2389493 2.1018629
## 5 2.828866 -1.8590252 -2.424163 1.4391942 -0.6173239 -1.5218846
## 6 -1.419639 0.7888914 1.996463 0.9813507 0.9034198 1.3810679
## stat113 stat114 stat115 stat116 stat117 stat118
## 1 -1.616161 1.0878664 0.9860094 -0.06288462 -1.013501 -1.2212842
## 2 -1.554771 1.8683100 0.4880588 -0.63865489 -1.610217 -1.7713343
## 3 -2.679801 -2.9486952 1.7753417 0.90311784 -1.318836 -0.1429040
## 4 2.459229 -0.5584171 0.4419581 -0.09586351 0.595442 0.2883342
## 5 -2.102200 1.6300170 -2.3498287 1.36771894 -1.912202 -0.2563821
## 6 -1.835037 0.6577786 -2.9928374 2.13540316 -1.437299 -0.9570006
## stat119 stat120 stat121 stat122 stat123 stat124
## 1 2.9222729 1.9151262 1.6686068 2.0061224 1.5723072 0.78819227
## 2 2.1828208 0.8283178 -2.4458632 1.7133740 1.1393738 -0.07182054
## 3 0.9721319 1.2723130 2.8002086 2.7670381 -2.2252586 2.17499113
## 4 -1.9327896 -2.5369370 1.7835028 1.0262097 -1.8790983 -0.43639564
## 5 1.3230809 -2.8145256 -0.9547533 -2.0435417 -0.2758764 -1.85668027
## 6 0.1720700 -1.4568460 1.4115051 -0.9878145 2.3895061 -2.33730745
## stat125 stat126 stat127 stat128 stat129 stat130
## 1 1.588372 1.1620011 -0.2474264 1.650328 2.5147598 0.37283245
## 2 -1.173771 0.8162020 0.3510315 -1.263667 1.7245284 -0.72852904
## 3 -1.503497 -0.5656394 2.8040256 -2.139287 -1.7221642 2.17899609
## 4 1.040967 -2.9039600 0.3103742 1.462339 -1.2940350 -2.95015502
## 5 -2.866184 1.6885070 -2.2525666 -2.628631 1.8581577 2.80127025
## 6 -1.355111 1.5017927 0.4295921 -0.580415 0.9851009 -0.03773117
## stat131 stat132 stat133 stat134 stat135 stat136
## 1 -0.09028241 0.5194538 2.8478346 2.6664724 -2.0206311 1.398415090
## 2 -0.53045595 1.4134049 2.9180586 0.3299096 1.4784122 -1.278896090
## 3 1.35843194 0.2279946 0.3532595 0.6138676 -0.3443284 0.057763811
## 4 -1.92450273 1.2698178 -1.5299660 -2.6083462 1.1665530 -0.187791914
## 5 1.49036849 2.6337729 -2.3206244 0.4978287 -1.7397571 0.001200184
## 6 -0.64642709 -1.9256228 1.7032650 -0.9152725 -0.3188055 2.155395980
## stat137 stat138 stat139 stat140 stat141 stat142
## 1 -1.2794871 0.4064890 -0.4539998 2.6660173 -1.8375313 0.4711883
## 2 -2.7709017 -1.6303773 -1.9025910 0.2572918 0.6612002 1.4764348
## 3 -1.1930757 -0.1051243 -0.5108380 -1.0879666 2.4969513 -0.9477230
## 4 -1.2318919 2.2348571 0.1788580 -1.5851788 -1.2384283 -2.1859181
## 5 1.8685058 2.7229517 -2.9077182 2.6606939 -1.5963592 -2.2213492
## 6 -0.4807318 -1.2117369 -0.9358531 -2.5100758 -2.3803916 -0.7096854
## stat143 stat144 stat145 stat146 stat147 stat148
## 1 1.9466263 2.2689433 -0.3597288 -0.6551386 1.65438592 0.6404466
## 2 1.3156421 2.4459090 -0.3790028 1.4858465 -0.07784461 1.0096149
## 3 0.1959563 2.3062942 1.8459278 2.6848175 -2.70935774 -1.2093409
## 4 1.7633296 -2.8171508 2.0902622 -2.6625464 -1.12600601 -2.1926479
## 5 0.3885758 1.8160636 2.8257299 -1.4526173 1.60679603 2.3807991
## 6 0.7623450 0.2692145 -2.4307463 -2.1244523 -2.67803812 -1.5273387
## stat149 stat150 stat151 stat152 stat153 stat154
## 1 0.1583575 0.4755351 0.3213410 2.0241520 1.5720103 -0.1825875
## 2 -0.4311406 2.9577663 0.6937252 0.1397280 0.3775735 -1.1012636
## 3 -0.8352824 2.5716205 1.7528236 0.4326277 -2.2334397 -2.6265771
## 4 -2.8069143 1.8813509 2.3358023 0.1015632 1.2117474 -1.3714278
## 5 -1.6166265 1.1112266 -1.1998471 2.9316769 -2.1676455 -0.3411089
## 6 -0.2265472 2.7264354 -1.6746094 -2.3376281 -1.7022788 -1.2352397
## stat155 stat156 stat157 stat158 stat159 stat160
## 1 -1.139657 0.07061254 0.5893906 -1.9920996 -2.83714366 2.249398
## 2 -2.041093 0.74047768 2.5415072 -1.2697256 -1.64364433 -2.448922
## 3 -1.219507 -0.55198693 0.4046920 1.2098547 -0.90412390 -1.934093
## 4 2.992191 2.33222485 2.0622969 -0.6714653 2.76836085 -1.431120
## 5 -2.362356 -1.23906672 0.4746319 -0.7849202 0.69399995 2.052411
## 6 -1.604499 1.31051409 -0.5164744 0.6288667 0.07899523 -2.287402
## stat161 stat162 stat163 stat164 stat165 stat166
## 1 1.7182635 -1.2323593 2.7350423 1.0707235 1.1621544 0.9493989
## 2 -0.6247674 2.6740098 2.8211024 1.5561292 -1.1027147 1.0519739
## 3 -0.6230453 -0.7993517 -2.8318374 -1.1148673 1.4261659 0.5294309
## 4 1.7644744 0.1696584 1.2653207 0.6621516 0.9470508 0.1985014
## 5 -1.2070210 0.7243784 0.9736322 2.7426259 -2.6862383 1.6840212
## 6 2.3705316 -2.1667893 -0.2516685 -0.8425958 -1.9099342 -2.8607297
## stat167 stat168 stat169 stat170 stat171 stat172
## 1 0.1146510 2.3872008 1.1180918 -0.95370555 -2.25076509 0.2348182
## 2 1.0760417 -2.0449336 0.9715676 -0.40173489 -0.11953555 -2.3107369
## 3 1.1735898 1.3860190 -2.2894719 0.06350347 0.29191551 -1.6079744
## 4 2.5511832 0.5446648 1.2694012 -0.84571201 0.79789722 0.2623538
## 5 2.2900002 2.6289782 -0.2783571 1.39032829 -0.55532032 1.0499046
## 6 -0.7513983 2.9617066 -2.2119520 -1.71958113 -0.01452018 -0.2751517
## stat173 stat174 stat175 stat176 stat177 stat178
## 1 1.79366076 -1.920206 -0.38841942 0.8530301 1.64532077 -1.1354179
## 2 -0.07484659 1.337846 2.20911694 0.9616837 -2.80810070 -2.1136749
## 3 -1.05521810 -1.483741 0.06148359 2.3066039 -0.34688616 1.1840581
## 4 0.31460321 1.195741 2.97633862 1.1685091 -0.06346265 1.4205489
## 5 -1.39428365 2.458523 0.64836472 -1.0396386 -0.57828104 -0.5006818
## 6 2.31844401 1.239864 -2.06490874 0.7696204 -1.77586019 2.0855925
## stat179 stat180 stat181 stat182 stat183 stat184
## 1 2.0018647 0.1476815 -1.27279520 1.9181504 -0.5297624 -2.9718938
## 2 -2.1351449 2.9012582 -1.09914911 -2.5488517 -2.8377736 1.4073374
## 3 -1.7819908 2.9902627 0.81908613 0.2503852 0.3712984 -2.1714024
## 4 -0.1026974 -2.4763253 -2.52645421 1.3096315 2.1458161 -1.5228094
## 5 -2.2298794 2.4465680 -0.70346898 -1.6997617 2.9178164 -0.3615532
## 6 -1.1168108 1.5552123 -0.01361342 1.7338791 -1.1104763 0.1882416
## stat185 stat186 stat187 stat188 stat189 stat190
## 1 -0.1043832 -1.5047463 2.700351 -2.4780862 -1.9078265 0.9978108
## 2 -2.0310574 -0.5380074 -1.963275 -1.2221278 -2.4290681 -1.9515115
## 3 2.6727278 1.2688179 -1.399018 -2.9612138 2.6456394 2.0073323
## 4 -2.7796295 2.0682354 2.243727 0.4296881 0.1931333 2.2710960
## 5 -0.6231265 2.5833981 2.229041 0.8139584 1.4544131 1.8886451
## 6 2.7204690 -2.4469144 -1.421998 1.7477882 -0.1481806 0.6011560
## stat191 stat192 stat193 stat194 stat195 stat196
## 1 -0.6644351 2.6270833 -1.1094601 -2.4200392 2.870713 -0.6590932
## 2 -0.6483142 1.4519118 -0.1963493 -2.3025322 1.255608 2.1617947
## 3 -1.5457382 -0.2977442 -1.7045015 0.7962404 -1.696063 -1.4771117
## 4 -1.1780495 -2.9747574 -1.1471518 -1.2377013 -1.010672 -2.6055975
## 5 2.8813178 -1.8964081 -1.2653487 -1.7839754 -2.872581 2.3033464
## 6 0.4437973 0.6599325 -1.4029555 -2.3118258 -1.792232 1.3934380
## stat197 stat198 stat199 stat200 stat201 stat202
## 1 -0.83056986 0.9550526 -1.7025776 -2.8263099 -0.7023998 0.2272806
## 2 -1.42178249 -1.2471864 2.5723093 -0.0233496 -1.8975239 1.9472262
## 3 -0.19233958 -0.5161456 0.0279946 -1.2333704 -2.9672263 -2.8666208
## 4 -1.23145902 1.4728470 -0.4562025 -2.2983441 -1.5101184 0.2530525
## 5 1.85018563 -1.8269292 -0.6337969 -2.1473246 0.9909850 1.0950903
## 6 -0.09311061 0.5144456 -2.8178268 -2.7555969 -2.3546004 -1.0558939
## stat203 stat204 stat205 stat206 stat207 stat208
## 1 1.166631220 0.007453276 2.9961641 1.5327307 -2.2293356 -0.9946009
## 2 -0.235396504 2.132749800 0.3707606 1.5604026 -1.0089217 2.1474257
## 3 0.003180946 2.229793310 2.7354040 0.8992231 2.9694967 2.3081024
## 4 -0.474482715 -1.584772230 -2.3224132 -0.9409741 -2.3179255 0.8032548
## 5 2.349412920 -1.276320220 -2.0203719 -1.1733509 1.0371852 -2.5086207
## 6 0.727436960 -0.960191786 -0.8964998 -1.6406623 -0.2330488 1.7993879
## stat209 stat210 stat211 stat212 stat213 stat214
## 1 -2.2182105 -1.4099774 -1.656754 2.6602585 -2.9270992 1.1240714
## 2 -2.8932488 -1.1641679 -2.605423 -1.5650513 2.9523673 2.0266318
## 3 -1.8279589 0.0472350 -2.026734 2.5054367 0.9903042 0.3274105
## 4 -1.0878067 0.1171303 2.645891 -1.6775225 1.3452160 1.4694063
## 5 -0.8158175 0.4060950 0.912256 0.2925677 2.1610141 0.5679936
## 6 -2.2664354 -0.2061083 -1.435174 2.6645632 0.4216259 -0.6419122
## stat215 stat216 stat217
## 1 -2.7510750 -0.5501796 1.2638469
## 2 2.8934650 -2.4099574 -1.2411407
## 3 -1.0947676 1.2852937 1.5411530
## 4 0.6343777 0.1345372 2.9102673
## 5 0.9908702 1.7909757 -2.0902610
## 6 -2.8113887 -1.0624912 0.2765074head(features.highprec)## JobName x1 x2 x3 x4 x5 x6
## 1 Job_00001 2.0734508 4.917267 19.96188 3.520878 7.861051 1.6067589
## 2 Job_00002 2.2682543 4.955773 19.11939 19.763031 6.931355 1.3622041
## 3 Job_00003 1.7424456 2.059819 13.37912 38.829132 6.274053 2.0529845
## 4 Job_00004 0.7873555 2.613983 17.23044 64.402557 5.377652 0.9067419
## 5 Job_00005 2.3342753 4.299076 14.64883 52.537304 6.793368 2.4605792
## 6 Job_00006 1.2365089 2.795370 11.13127 96.819939 6.583971 2.3510606
## x7 x8 x9 x10 x11 x12 x13
## 1 2.979479 8.537228 1.103368 4.6089458 1.050025e-07 7.995825 13.215498
## 2 2.388119 6.561461 0.588572 1.0283282 1.034518e-07 7.486966 22.557224
## 3 2.043592 10.275595 4.834385 4.3872848 1.062312e-07 6.350142 15.049810
## 4 2.395118 13.487331 3.340190 4.5053501 9.471887e-08 9.548698 17.170635
## 5 2.891535 9.362389 1.246039 1.7333300 1.010552e-07 9.596095 5.794567
## 6 1.247838 7.033354 1.852231 0.4839371 1.071662e-07 3.810983 23.863169
## x14 x15 x16 x17 x18 x19 x20
## 1 4.377983 0.2370623 6.075459 3.988347 4.767475 2.698775 1.035893
## 2 2.059315 0.5638121 6.903891 4.152054 6.849232 9.620731 1.915288
## 3 3.260057 2.0603445 8.424065 4.489893 3.493591 4.715386 1.558103
## 4 3.093478 1.8806034 11.189792 2.134271 5.588357 5.107871 1.489588
## 5 3.943076 1.5820830 7.096742 3.563378 7.765610 1.360272 1.240283
## 6 1.280562 1.1733382 7.062051 1.341864 7.748325 5.009365 1.725179
## x21 x22 x23 stat1 stat2 stat3 stat4
## 1 42.36548 1.356213 2.699796 2.3801832 0.1883335 -1.2284011 -0.5999233
## 2 26.63295 4.053961 2.375127 -1.4069480 1.8140973 1.6204884 2.6422672
## 3 20.09693 3.079888 4.488420 -0.7672566 -0.1230289 1.1415752 2.9805934
## 4 32.60415 1.355396 3.402398 0.4371202 -1.9355906 0.9028624 -1.6025400
## 5 44.58361 1.940301 2.249011 2.4492466 -0.6172000 -2.5520642 -2.1485929
## 6 28.75102 2.500499 5.563972 -1.7899084 1.8853619 2.4154840 -2.6022179
## stat5 stat6 stat7 stat8 stat9 stat10
## 1 0.148893163 -0.6622978 -2.4851868 0.3647782 2.5364335 2.92067981
## 2 1.920768980 1.7411555 -1.9599979 -2.0190558 -1.3732762 -0.31642506
## 3 2.422584300 -0.4166040 2.2205689 -2.6741531 0.4844292 2.73379230
## 4 -0.001795933 -0.6946563 -0.3693534 -0.9709467 1.7960306 0.74771154
## 5 -2.311132430 -1.0166832 2.7269876 1.5424492 -1.3156369 -0.09767897
## 6 -1.785491470 -1.8599915 1.4875095 2.0188572 -1.4892503 -1.41103566
## stat11 stat12 stat13 stat14 stat15 stat16
## 1 -2.3228905 -2.480567 -0.6335157 -0.3650149 -0.5322812 0.6029300
## 2 -0.8547903 1.119316 0.7227427 0.2121097 -0.1452281 -2.0361528
## 3 -2.1821580 2.865401 -2.9756081 2.9871745 1.9539525 -1.8857163
## 4 1.3982378 1.856765 -1.0379983 2.3341896 2.3057184 -2.8947697
## 5 0.9567220 2.567549 0.3184886 1.0307668 0.1644241 -0.6613821
## 6 0.5341771 -1.461822 0.4402476 -1.9282095 -0.3680157 1.8188807
## stat17 stat18 stat19 stat20 stat21 stat22
## 1 -1.04516208 2.3544915 2.4049001 0.2633883 -0.9788178 1.7868229
## 2 0.09513074 0.4727738 1.8899702 2.7892542 -1.3919091 -1.7198164
## 3 0.40285346 1.4655282 -1.4952788 2.9162340 -2.3893208 2.8161423
## 4 2.97446084 2.3896182 2.3083484 -1.1894441 -2.1982553 1.3666242
## 5 -0.98465055 0.6900643 1.5894209 -2.1204538 1.7961155 -0.9362189
## 6 -1.45726359 -2.1139548 -0.3964904 1.1764175 -2.9100556 -2.1359294
## stat23 stat24 stat25 stat26 stat27 stat28
## 1 -2.3718851 2.8580718 -0.4719713 -2.817086 -0.9518474 2.88892484
## 2 -2.3293245 1.5577759 -1.9569720 1.554194 -0.5081459 -1.58715141
## 3 -2.5402296 0.1422861 0.3572798 -1.051886 -2.1541717 0.03074004
## 4 -1.9679050 -1.4077642 2.5097435 1.683121 -0.2549745 -2.90384054
## 5 2.0523429 -2.2084844 -1.9280857 -2.116736 1.8180779 -1.42167580
## 6 0.2184991 -0.7599817 2.6880329 -2.903350 -1.0733233 -2.92416644
## stat29 stat30 stat31 stat32 stat33 stat34
## 1 0.7991088 -2.0059092 -0.2461502 0.6482101 -2.87462163 -0.3601543
## 2 1.9758110 -0.3874187 1.3566630 2.6493473 2.28463054 1.8591728
## 3 -0.4460218 1.0279679 1.3998452 -1.0183365 1.41109037 -2.4183984
## 4 1.0571996 2.5588036 -2.9830337 -1.1299983 0.05470414 -1.5566561
## 5 0.8854889 2.2774174 2.6499031 2.3053405 -2.39148426 -1.8272992
## 6 -0.8405267 0.1311945 0.4321289 -2.9622040 -2.55387473 2.6396458
## stat35 stat36 stat37 stat38 stat39 stat40
## 1 2.4286051 -0.5420244 -2.6782637 -2.8874269 -0.8945006 1.1749642
## 2 1.3709245 -1.3714181 1.3901204 1.2273489 -0.8934880 1.0540369
## 3 -0.9805572 2.0571353 0.8845031 2.0574493 1.1222047 1.8528618
## 4 1.0969149 -2.2820673 1.8852408 0.5391517 2.7334342 -0.4372566
## 5 -1.0971669 1.4867796 -2.3738465 -0.3743561 1.4266498 1.2551680
## 6 0.4584349 -2.2696617 -0.9935142 -0.5350499 -0.7874799 2.0009417
## stat41 stat42 stat43 stat44 stat45 stat46
## 1 -1.0474428 -1.3909023 2.54110503 -1.4320793 0.6298335 -2.09296608
## 2 2.5380247 1.6476108 0.44128850 -2.5049477 1.2726039 1.72492969
## 3 1.1477574 0.2288794 0.08891252 2.3044751 -0.7735722 -0.07302936
## 4 -1.3808300 -2.7900956 2.38297582 0.1686397 -2.1591296 1.60828602
## 5 0.2257536 1.9542116 2.66429019 0.8026123 -1.5521187 1.61751962
## 6 -1.3364114 -2.2898803 2.80735397 -0.8413086 1.0057797 -1.50653386
## stat47 stat48 stat49 stat50 stat51 stat52
## 1 -2.8318939 2.1445766 0.5668035 0.1544579 0.6291955 2.2197027
## 2 -0.5804687 -1.3689737 1.4908396 1.2465997 0.8896304 -2.6024318
## 3 0.7918019 1.5712964 1.1038082 -0.2545658 -2.1662638 0.2660159
## 4 -1.8894132 0.5680230 -0.7023218 -0.3972188 0.1578027 2.1770194
## 5 2.1088455 -2.7195437 2.1961412 -0.2615084 1.2109556 0.8260623
## 6 -1.4400891 -0.9421459 -1.7324599 -2.1720727 -2.8129435 0.6958785
## stat53 stat54 stat55 stat56 stat57 stat58
## 1 2.176805 0.5546907 -2.19704103 -0.2884173 1.3232913 -1.32824039
## 2 -2.107441 1.3864788 0.08781975 1.9998228 0.8014438 -0.26979154
## 3 1.234197 2.1337581 1.65231645 -0.4388691 -0.1811156 2.11277962
## 4 2.535406 -2.1387620 0.12856023 -1.9906180 0.9626449 1.65232646
## 5 -2.457080 2.1633499 0.60441124 2.5449364 -1.4978440 2.60542655
## 6 2.003033 -0.5379940 -2.19647264 -1.1954677 -0.5974466 -0.04703835
## stat59 stat60 stat61 stat62 stat63 stat64
## 1 1.24239659 -2.5798278 1.327928 1.68560362 0.6284891 -1.6798652
## 2 0.06379301 0.9465770 1.116928 0.03128772 -2.1944375 0.3382609
## 3 0.93223447 2.4597080 0.465251 -1.71033382 -0.5156728 1.8276784
## 4 -0.29840910 0.7273473 -2.313066 -1.47696018 2.5910559 -1.5127999
## 5 -1.17610002 -1.7948418 -2.669305 0.17813617 2.8956099 2.9411416
## 6 -1.01793981 0.2817057 2.228023 -0.86494124 -0.9747949 -0.1569053
## stat65 stat66 stat67 stat68 stat69 stat70
## 1 -2.9490898 -0.3325469 1.5745990 -2.2978280 1.5451891 -1.345990
## 2 -1.1174885 -1.5728682 -2.9229002 0.2658547 -1.9616533 2.506130
## 3 -0.2231264 -0.4503301 0.7932286 -1.2453773 -2.2309763 2.309761
## 4 -0.3522418 -2.0720532 0.9442933 2.9212906 0.5100371 -2.441108
## 5 -2.1648991 1.2002029 2.8266985 0.7461294 1.6772674 -1.280000
## 6 -2.2295458 1.1446493 0.2024925 -0.2983998 -2.8203752 1.224030
## stat71 stat72 stat73 stat74 stat75 stat76
## 1 1.0260956 2.1071210 2.6625669 -2.8924677 -0.02132523 -2.5058765
## 2 0.3525076 1.6922342 -1.2167022 -1.7271879 2.21176434 1.9329683
## 3 -2.1799035 -2.2645276 0.1415582 0.9887453 1.95592320 0.2951785
## 4 -2.4051409 2.0876484 -0.8632146 0.4011389 -1.16986716 -1.2391174
## 5 1.3538754 -0.8089395 -0.5122626 -2.1696892 1.07344925 2.6696169
## 6 -2.8073371 -1.4450488 0.5481212 -1.4381690 0.80917043 -0.1365944
## stat77 stat78 stat79 stat80 stat81 stat82
## 1 -2.5631845 -2.40331340 0.38416120 -1.2564875 -0.1550840 -1.1762617
## 2 -0.4462085 0.38400793 1.80483031 -0.8387642 0.7624431 0.9936900
## 3 1.6757870 -1.81900752 2.70904708 -0.3201959 2.5754235 1.6346260
## 4 -2.1012006 -2.24691081 1.78056848 1.0323739 1.0762523 2.1343851
## 5 -2.5736733 -1.99958372 -0.05388495 -2.5630073 -2.8783002 -0.5752426
## 6 1.6143972 0.03233746 2.90835762 1.4000487 2.9275615 -2.8503830
## stat83 stat84 stat85 stat86 stat87 stat88
## 1 1.2840565 -2.6794965 1.3956039 -1.5290235 2.221152 2.3794982
## 2 -0.2380048 1.9314318 -1.6747955 -0.3663656 1.582659 -0.5222489
## 3 -0.9150769 -1.5520337 2.4186287 2.7273662 1.306642 0.1320062
## 4 -2.5824408 -2.7775943 0.5085060 0.4689015 2.053348 0.7957955
## 5 -1.0017741 -0.2009138 0.3770109 2.4335201 -1.118058 1.3953410
## 6 2.4891765 2.9931953 -1.4171852 0.3905659 -1.856119 -2.1690490
## stat89 stat90 stat91 stat92 stat93 stat94
## 1 -0.9885110 -0.8873261 -2.7810929 -1.53325891 2.6002395 1.8890998
## 2 0.9982028 -1.2382015 -0.1574496 0.41086048 -0.5412626 -0.2421387
## 3 0.5956759 1.6871066 2.2452753 2.74279594 -1.5860478 2.9393122
## 4 2.0902634 2.1752586 -2.0677712 -2.37861037 1.1653302 0.1500632
## 5 2.9820614 0.8111660 -0.7842287 0.03766387 -1.1681970 2.1217251
## 6 -1.7428021 0.1579032 1.7456742 -0.36858466 -0.1304616 -1.4555819
## stat95 stat96 stat97 stat98 stat99 stat100
## 1 -2.6056035 -0.5814857 2.57652426 -2.3297751 2.6324007 1.445827
## 2 -2.0271583 -0.9126074 2.49582648 0.9745382 1.1339203 -2.549544
## 3 0.3823181 -0.6324139 2.46221566 1.1151560 0.4624891 0.107072
## 4 2.6414623 -0.6630505 2.10394859 1.2627635 0.4861740 1.697012
## 5 1.4642254 2.6485956 -0.07699547 0.6219473 -1.8815142 -2.685463
## 6 1.8937331 -0.4690555 1.04671776 -0.5879866 -0.9766789 2.405940
## stat101 stat102 stat103 stat104 stat105 stat106
## 1 -2.1158021 2.603936 1.7745128 -1.8903574 -1.8558655 1.0122044
## 2 -2.7998588 -2.267895 0.5336456 -0.2859477 -0.5196246 -0.9417582
## 3 0.7969509 -1.744906 -0.7960327 1.9767258 -0.2007264 -0.7872376
## 4 1.7071959 -1.540221 1.6770362 1.5395796 -0.4855365 -1.2894115
## 5 -1.4627420 -1.700983 2.4376490 0.2731541 1.5275587 1.3256483
## 6 2.6888530 1.090155 2.0769854 1.9615480 1.8689761 2.8975825
## stat107 stat108 stat109 stat110 stat111 stat112
## 1 1.954508 -0.3376471 2.503084 0.3099165 2.7209847 -2.3911204
## 2 -2.515160 0.3998704 -1.077093 2.4228268 -0.7759693 0.2513882
## 3 1.888827 1.5819857 -2.066659 -2.0008364 0.6997684 2.6157095
## 4 1.076395 -1.8524148 -2.689204 1.0985872 1.2389493 2.1018629
## 5 2.828866 -1.8590252 -2.424163 1.4391942 -0.6173239 -1.5218846
## 6 -1.419639 0.7888914 1.996463 0.9813507 0.9034198 1.3810679
## stat113 stat114 stat115 stat116 stat117 stat118
## 1 -1.616161 1.0878664 0.9860094 -0.06288462 -1.013501 -1.2212842
## 2 -1.554771 1.8683100 0.4880588 -0.63865489 -1.610217 -1.7713343
## 3 -2.679801 -2.9486952 1.7753417 0.90311784 -1.318836 -0.1429040
## 4 2.459229 -0.5584171 0.4419581 -0.09586351 0.595442 0.2883342
## 5 -2.102200 1.6300170 -2.3498287 1.36771894 -1.912202 -0.2563821
## 6 -1.835037 0.6577786 -2.9928374 2.13540316 -1.437299 -0.9570006
## stat119 stat120 stat121 stat122 stat123 stat124
## 1 2.9222729 1.9151262 1.6686068 2.0061224 1.5723072 0.78819227
## 2 2.1828208 0.8283178 -2.4458632 1.7133740 1.1393738 -0.07182054
## 3 0.9721319 1.2723130 2.8002086 2.7670381 -2.2252586 2.17499113
## 4 -1.9327896 -2.5369370 1.7835028 1.0262097 -1.8790983 -0.43639564
## 5 1.3230809 -2.8145256 -0.9547533 -2.0435417 -0.2758764 -1.85668027
## 6 0.1720700 -1.4568460 1.4115051 -0.9878145 2.3895061 -2.33730745
## stat125 stat126 stat127 stat128 stat129 stat130
## 1 1.588372 1.1620011 -0.2474264 1.650328 2.5147598 0.37283245
## 2 -1.173771 0.8162020 0.3510315 -1.263667 1.7245284 -0.72852904
## 3 -1.503497 -0.5656394 2.8040256 -2.139287 -1.7221642 2.17899609
## 4 1.040967 -2.9039600 0.3103742 1.462339 -1.2940350 -2.95015502
## 5 -2.866184 1.6885070 -2.2525666 -2.628631 1.8581577 2.80127025
## 6 -1.355111 1.5017927 0.4295921 -0.580415 0.9851009 -0.03773117
## stat131 stat132 stat133 stat134 stat135 stat136
## 1 -0.09028241 0.5194538 2.8478346 2.6664724 -2.0206311 1.398415090
## 2 -0.53045595 1.4134049 2.9180586 0.3299096 1.4784122 -1.278896090
## 3 1.35843194 0.2279946 0.3532595 0.6138676 -0.3443284 0.057763811
## 4 -1.92450273 1.2698178 -1.5299660 -2.6083462 1.1665530 -0.187791914
## 5 1.49036849 2.6337729 -2.3206244 0.4978287 -1.7397571 0.001200184
## 6 -0.64642709 -1.9256228 1.7032650 -0.9152725 -0.3188055 2.155395980
## stat137 stat138 stat139 stat140 stat141 stat142
## 1 -1.2794871 0.4064890 -0.4539998 2.6660173 -1.8375313 0.4711883
## 2 -2.7709017 -1.6303773 -1.9025910 0.2572918 0.6612002 1.4764348
## 3 -1.1930757 -0.1051243 -0.5108380 -1.0879666 2.4969513 -0.9477230
## 4 -1.2318919 2.2348571 0.1788580 -1.5851788 -1.2384283 -2.1859181
## 5 1.8685058 2.7229517 -2.9077182 2.6606939 -1.5963592 -2.2213492
## 6 -0.4807318 -1.2117369 -0.9358531 -2.5100758 -2.3803916 -0.7096854
## stat143 stat144 stat145 stat146 stat147 stat148
## 1 1.9466263 2.2689433 -0.3597288 -0.6551386 1.65438592 0.6404466
## 2 1.3156421 2.4459090 -0.3790028 1.4858465 -0.07784461 1.0096149
## 3 0.1959563 2.3062942 1.8459278 2.6848175 -2.70935774 -1.2093409
## 4 1.7633296 -2.8171508 2.0902622 -2.6625464 -1.12600601 -2.1926479
## 5 0.3885758 1.8160636 2.8257299 -1.4526173 1.60679603 2.3807991
## 6 0.7623450 0.2692145 -2.4307463 -2.1244523 -2.67803812 -1.5273387
## stat149 stat150 stat151 stat152 stat153 stat154
## 1 0.1583575 0.4755351 0.3213410 2.0241520 1.5720103 -0.1825875
## 2 -0.4311406 2.9577663 0.6937252 0.1397280 0.3775735 -1.1012636
## 3 -0.8352824 2.5716205 1.7528236 0.4326277 -2.2334397 -2.6265771
## 4 -2.8069143 1.8813509 2.3358023 0.1015632 1.2117474 -1.3714278
## 5 -1.6166265 1.1112266 -1.1998471 2.9316769 -2.1676455 -0.3411089
## 6 -0.2265472 2.7264354 -1.6746094 -2.3376281 -1.7022788 -1.2352397
## stat155 stat156 stat157 stat158 stat159 stat160
## 1 -1.139657 0.07061254 0.5893906 -1.9920996 -2.83714366 2.249398
## 2 -2.041093 0.74047768 2.5415072 -1.2697256 -1.64364433 -2.448922
## 3 -1.219507 -0.55198693 0.4046920 1.2098547 -0.90412390 -1.934093
## 4 2.992191 2.33222485 2.0622969 -0.6714653 2.76836085 -1.431120
## 5 -2.362356 -1.23906672 0.4746319 -0.7849202 0.69399995 2.052411
## 6 -1.604499 1.31051409 -0.5164744 0.6288667 0.07899523 -2.287402
## stat161 stat162 stat163 stat164 stat165 stat166
## 1 1.7182635 -1.2323593 2.7350423 1.0707235 1.1621544 0.9493989
## 2 -0.6247674 2.6740098 2.8211024 1.5561292 -1.1027147 1.0519739
## 3 -0.6230453 -0.7993517 -2.8318374 -1.1148673 1.4261659 0.5294309
## 4 1.7644744 0.1696584 1.2653207 0.6621516 0.9470508 0.1985014
## 5 -1.2070210 0.7243784 0.9736322 2.7426259 -2.6862383 1.6840212
## 6 2.3705316 -2.1667893 -0.2516685 -0.8425958 -1.9099342 -2.8607297
## stat167 stat168 stat169 stat170 stat171 stat172
## 1 0.1146510 2.3872008 1.1180918 -0.95370555 -2.25076509 0.2348182
## 2 1.0760417 -2.0449336 0.9715676 -0.40173489 -0.11953555 -2.3107369
## 3 1.1735898 1.3860190 -2.2894719 0.06350347 0.29191551 -1.6079744
## 4 2.5511832 0.5446648 1.2694012 -0.84571201 0.79789722 0.2623538
## 5 2.2900002 2.6289782 -0.2783571 1.39032829 -0.55532032 1.0499046
## 6 -0.7513983 2.9617066 -2.2119520 -1.71958113 -0.01452018 -0.2751517
## stat173 stat174 stat175 stat176 stat177 stat178
## 1 1.79366076 -1.920206 -0.38841942 0.8530301 1.64532077 -1.1354179
## 2 -0.07484659 1.337846 2.20911694 0.9616837 -2.80810070 -2.1136749
## 3 -1.05521810 -1.483741 0.06148359 2.3066039 -0.34688616 1.1840581
## 4 0.31460321 1.195741 2.97633862 1.1685091 -0.06346265 1.4205489
## 5 -1.39428365 2.458523 0.64836472 -1.0396386 -0.57828104 -0.5006818
## 6 2.31844401 1.239864 -2.06490874 0.7696204 -1.77586019 2.0855925
## stat179 stat180 stat181 stat182 stat183 stat184
## 1 2.0018647 0.1476815 -1.27279520 1.9181504 -0.5297624 -2.9718938
## 2 -2.1351449 2.9012582 -1.09914911 -2.5488517 -2.8377736 1.4073374
## 3 -1.7819908 2.9902627 0.81908613 0.2503852 0.3712984 -2.1714024
## 4 -0.1026974 -2.4763253 -2.52645421 1.3096315 2.1458161 -1.5228094
## 5 -2.2298794 2.4465680 -0.70346898 -1.6997617 2.9178164 -0.3615532
## 6 -1.1168108 1.5552123 -0.01361342 1.7338791 -1.1104763 0.1882416
## stat185 stat186 stat187 stat188 stat189 stat190
## 1 -0.1043832 -1.5047463 2.700351 -2.4780862 -1.9078265 0.9978108
## 2 -2.0310574 -0.5380074 -1.963275 -1.2221278 -2.4290681 -1.9515115
## 3 2.6727278 1.2688179 -1.399018 -2.9612138 2.6456394 2.0073323
## 4 -2.7796295 2.0682354 2.243727 0.4296881 0.1931333 2.2710960
## 5 -0.6231265 2.5833981 2.229041 0.8139584 1.4544131 1.8886451
## 6 2.7204690 -2.4469144 -1.421998 1.7477882 -0.1481806 0.6011560
## stat191 stat192 stat193 stat194 stat195 stat196
## 1 -0.6644351 2.6270833 -1.1094601 -2.4200392 2.870713 -0.6590932
## 2 -0.6483142 1.4519118 -0.1963493 -2.3025322 1.255608 2.1617947
## 3 -1.5457382 -0.2977442 -1.7045015 0.7962404 -1.696063 -1.4771117
## 4 -1.1780495 -2.9747574 -1.1471518 -1.2377013 -1.010672 -2.6055975
## 5 2.8813178 -1.8964081 -1.2653487 -1.7839754 -2.872581 2.3033464
## 6 0.4437973 0.6599325 -1.4029555 -2.3118258 -1.792232 1.3934380
## stat197 stat198 stat199 stat200 stat201 stat202
## 1 -0.83056986 0.9550526 -1.7025776 -2.8263099 -0.7023998 0.2272806
## 2 -1.42178249 -1.2471864 2.5723093 -0.0233496 -1.8975239 1.9472262
## 3 -0.19233958 -0.5161456 0.0279946 -1.2333704 -2.9672263 -2.8666208
## 4 -1.23145902 1.4728470 -0.4562025 -2.2983441 -1.5101184 0.2530525
## 5 1.85018563 -1.8269292 -0.6337969 -2.1473246 0.9909850 1.0950903
## 6 -0.09311061 0.5144456 -2.8178268 -2.7555969 -2.3546004 -1.0558939
## stat203 stat204 stat205 stat206 stat207 stat208
## 1 1.166631220 0.007453276 2.9961641 1.5327307 -2.2293356 -0.9946009
## 2 -0.235396504 2.132749800 0.3707606 1.5604026 -1.0089217 2.1474257
## 3 0.003180946 2.229793310 2.7354040 0.8992231 2.9694967 2.3081024
## 4 -0.474482715 -1.584772230 -2.3224132 -0.9409741 -2.3179255 0.8032548
## 5 2.349412920 -1.276320220 -2.0203719 -1.1733509 1.0371852 -2.5086207
## 6 0.727436960 -0.960191786 -0.8964998 -1.6406623 -0.2330488 1.7993879
## stat209 stat210 stat211 stat212 stat213 stat214
## 1 -2.2182105 -1.4099774 -1.656754 2.6602585 -2.9270992 1.1240714
## 2 -2.8932488 -1.1641679 -2.605423 -1.5650513 2.9523673 2.0266318
## 3 -1.8279589 0.0472350 -2.026734 2.5054367 0.9903042 0.3274105
## 4 -1.0878067 0.1171303 2.645891 -1.6775225 1.3452160 1.4694063
## 5 -0.8158175 0.4060950 0.912256 0.2925677 2.1610141 0.5679936
## 6 -2.2664354 -0.2061083 -1.435174 2.6645632 0.4216259 -0.6419122
## stat215 stat216 stat217
## 1 -2.7510750 -0.5501796 1.2638469
## 2 2.8934650 -2.4099574 -1.2411407
## 3 -1.0947676 1.2852937 1.5411530
## 4 0.6343777 0.1345372 2.9102673
## 5 0.9908702 1.7909757 -2.0902610
## 6 -2.8113887 -1.0624912 0.2765074features = features.highprec
#str(features) Checking correlations to evaluate removal of redundant features
corr.matrix = round(cor(features[sapply(features, is.numeric)]),2)
# filter out only highly correlated variables
threshold = 0.6
corr.matrix.tmp = corr.matrix
diag(corr.matrix.tmp) = 0
high.corr = apply(abs(corr.matrix.tmp) >= threshold, 1, any)
high.corr.matrix = corr.matrix.tmp[high.corr, high.corr]
DT::datatable(corr.matrix)DT::datatable(high.corr.matrix)Feature Names
feature.names = colnames(features)
drops <- c('JobName')
feature.names = feature.names[!(feature.names %in% drops)]
#str(feature.names)Read and Clean Labels
labels = read.csv("../../Data/labels.csv")
#str(labels)
labels = labels[,c("JobName", output.var)]
summary(labels)## JobName y3
## Job_00001: 1 Min. : 95.91
## Job_00002: 1 1st Qu.:118.21
## Job_00003: 1 Median :123.99
## Job_00004: 1 Mean :125.36
## Job_00005: 1 3rd Qu.:131.06
## Job_00006: 1 Max. :193.73
## (Other) :9994 NA's :2497Merge Datasets
data <- merge(features, labels, by = 'JobName')
drops <- c('JobName')
data = data[,(!colnames(data) %in% drops)]
#str(data)Transformations
if (transform.abs == TRUE){
data[,label.names] = 10^(data[,label.names]/20)
data = filter(data, y3 < 1E7)
}
#str(data)
if (log.pred == TRUE){
data[label.names] = log(data[alt.scale.label.name],10)
drops = c(alt.scale.label.name)
data = data[!(names(data) %in% drops)]
}
#str(data)Remove NA Cases
data = data[complete.cases(data),]Exploratory Data Analysis
Check correlation of Label with Featires
if (eda == TRUE){
corr.to.label =round(cor(dplyr::select(data,-one_of(label.names)),dplyr::select_at(data,label.names)),4)
DT::datatable(corr.to.label)
}Multicollinearity - VIF
if (eda == TRUE){
vifDF = usdm::vif(select_at(data,feature.names)) %>% arrange(desc(VIF))
head(vifDF,10)
}Scatterplots
panel.hist <- function(x, ...)
{
usr <- par("usr"); on.exit(par(usr))
par(usr = c(usr[1:2], 0, 1.5) )
h <- hist(x, plot = FALSE)
breaks <- h$breaks; nB <- length(breaks)
y <- h$counts; y <- y/max(y)
rect(breaks[-nB], 0, breaks[-1], y, col = "cyan", ...)
}if (eda == TRUE){
histogram(data[ ,label.names])
#hist(data[complete.cases(data),alt.scale.label.name])
}# https://stackoverflow.com/questions/24648729/plot-one-numeric-variable-against-n-numeric-variables-in-n-plots
ind.pairs.plot <- function(data, xvars=NULL, yvar)
{
df <- data
if (is.null(xvars)) {
xvars = names(data[which(names(data)!=yvar)])
}
#choose a format to display charts
ncharts <- length(xvars)
for(i in 1:ncharts){
plot(df[,xvars[i]],df[,yvar], xlab = xvars[i], ylab = yvar)
}
}
if (eda == TRUE){
ind.pairs.plot(data, feature.names, label.names)
}
#
# pl <- ggplot(data, aes(x=x18, y = y3))
# pl2 <- pl + geom_point(aes(alpha = 0.1)) # default color gradient based on 'hp'
# print(pl2)Feature Engineering
if(eda ==FALSE){
# x18 may need transformations
plot(data[,'x18'], data[,label.names], main = "Original Scatter Plot vs. x18", ylab = label.names, xlab = 'x18')
plot(sqrt(data[,'x18']), data[,label.names], main = "Original Scatter Plot vs. sqrt(x18)", ylab = label.names, xlab = 'sqrt(x18)')
# transforming x18
data$sqrt.x18 = sqrt(data$x18)
data = dplyr::select(data,-one_of('x18'))
# what about x7, x9?
# x11 looks like data is at discrete points after a while. Will this be a problem?
}
Modeling
Train Test Split
data = data[sample(nrow(data)),] # randomly shuffle data
split = sample.split(data[,label.names], SplitRatio = 0.8)
data.train = subset(data, split == TRUE)
data.test = subset(data, split == FALSE)Common Functions
plot.diagnostics <- function(model, train) {
plot(model)
residuals = resid(model) # Plotted above in plot(lm.out)
r.standard = rstandard(model)
r.student = rstudent(model)
plot(predict(model,train),r.student,
ylab="Student Residuals", xlab="Predicted Values",
main="Student Residual Plot")
abline(0, 0)
plot(predict(model, train),r.standard,
ylab="Standard Residuals", xlab="Predicted Values",
main="Standard Residual Plot")
abline(0, 0)
abline(2, 0)
abline(-2, 0)
# Histogram
hist(r.student, freq=FALSE, main="Distribution of Studentized Residuals",
xlab="Studentized Residuals", ylab="Density", ylim=c(0,0.5))
# Create range of x-values for normal curve
xfit <- seq(min(r.student)-1, max(r.student)+1, length=40)
# Generate values from the normal distribution at the specified values
yfit <- (dnorm(xfit))
# Add the normal curve
lines(xfit, yfit, ylim=c(0,0.5))
# http://www.stat.columbia.edu/~martin/W2024/R7.pdf
# Influential plots
inf.meas = influence.measures(model)
# print (summary(inf.meas)) # too much data
# Leverage plot
lev = hat(model.matrix(model))
plot(lev, ylab = 'Leverage - check')
# Cook's Distance
cd = cooks.distance(model)
plot(cd,ylab="Cooks distances")
abline(4/nrow(train),0)
abline(1,0)
print (paste("Number of data points that have Cook's D > 4/n: ", length(cd[cd > 4/nrow(train)]), sep = ""))
print (paste("Number of data points that have Cook's D > 1: ", length(cd[cd > 1]), sep = ""))
return(cd)
}
train.caret.glmselect = function(formula, data, method
,subopt = NULL, feature.names
, train.control = NULL, tune.grid = NULL, pre.proc = NULL){
if(is.null(train.control)){
train.control <- trainControl(method = "cv"
,number = 10
,search = "grid"
,verboseIter = TRUE
,allowParallel = TRUE
)
}
if(is.null(tune.grid)){
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
tune.grid = data.frame(nvmax = 1:length(feature.names))
}
if (method == 'glmnet' && subopt == 'LASSO'){
# Will only show 1 Lambda value during training, but that is OK
# https://stackoverflow.com/questions/47526544/why-need-to-tune-lambda-with-carettrain-method-glmnet-and-cv-glmnet
# Another option for LASSO is this: https://github.com/topepo/caret/blob/master/RegressionTests/Code/lasso.R
lambda = 10^seq(-2,0, length =100)
alpha = c(1)
tune.grid = expand.grid(alpha = alpha,lambda = lambda)
}
if (method == 'lars'){
# https://github.com/topepo/caret/blob/master/RegressionTests/Code/lars.R
fraction = seq(0, 1, length = 100)
tune.grid = expand.grid(fraction = fraction)
pre.proc = c("center", "scale")
}
}
# http://sshaikh.org/2015/05/06/parallelize-machine-learning-in-r-with-multi-core-cpus/
cl <- makeCluster(detectCores()*0.75) # use 75% of cores only, leave rest for other tasks
registerDoParallel(cl)
set.seed(1)
# note that the seed has to actually be set just before this function is called
# settign is above just not ensure reproducibility for some reason
model.caret <- caret::train(formula
, data = data
, method = method
, tuneGrid = tune.grid
, trControl = train.control
, preProc = pre.proc
)
stopCluster(cl)
registerDoSEQ() # register sequential engine in case you are not using this function anymore
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
print(model.caret$results) # all model results
print(model.caret$bestTune) # best model
model = model.caret$finalModel
# Residuals Plot MMORO #
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth()
plot(residPlot)
# Provides the coefficients of the best model
id = rownames(model.caret$bestTune)
message("Coefficients of final model:")
print (coef(model, id = id))
# Need to find alternate to plotting diagnostic plots
# plot.diagnostics(model.forward,data.train)
# plot(model.forward,labels = colnames(data.train),scale=c("bic")) ## too many variables
return(list(model = model,id = id))
}
if (method == 'glmnet' && subopt == 'LASSO'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
# Residuals Plot #
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth()
plot(residPlot)
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id))
}
if (method == 'lars'){
print(model.caret)
print(plot(model.caret))
print(model.caret$bestTune)
# Residuals Plot #
dataPlot=data.frame(pred=predict(model.caret,data),res=resid(model.caret))
residPlot = ggplot(dataPlot,aes(x=pred,y=res)) +
geom_point(color='light blue',alpha=0.7) +
geom_smooth()
plot(residPlot)
id = NULL # not really needed but added for consistency
return(list(model = model.caret,id = id))
}
}
# https://stackoverflow.com/questions/48265743/linear-model-subset-selection-goodness-of-fit-with-k-fold-cross-validation
# changes slightly since call[[2]] was just returning "formula" without actually returnign the value in formula
predict.regsubsets <- function(object, newdata, id, formula, ...) {
#form <- as.formula(object$call[[2]])
mat <- model.matrix(formula, newdata) # adds intercept and expands any interaction terms
coefi <- coef(object, id = id)
xvars <- names(coefi)
return(mat[,xvars]%*%coefi)
}
test.model = function(model, test, level=0.95
,draw.limits = FALSE, good = 0.1, ok = 0.15
,method = NULL, subopt = NULL
,id = NULL, formula, feature.names, label.names){
## if using caret for glm select equivalent functionality,
## need to set regsubset = TRUE, pass id of best model through id variable,
## and pass formula (full is ok as it will select subset of variables from there)
if (is.null(method)){
pred = predict(model, newdata=test, interval="confidence", level = level)
}
if (method == 'leapForward' | method == 'leapBackward' | method == 'leapSeq'){
pred = predict.regsubsets(model, newdata = test, id = id, formula = formula)
}
if (method == 'glmnet' && subopt == 'LASSO'){
xtest = as.matrix(test[,feature.names])
pred=as.data.frame(predict(model, xtest))
}
if (method == 'lars'){
pred=as.data.frame(predict(model, newdata = test))
}
# Summary of predicted values
print ("Summary of predicted values: ")
print(summary(pred[,1]))
test.mse = mean((test[,label.names]-pred[,1])^2)
print (paste(method, subopt, "Test MSE:", test.mse, sep=" "))
plot(test[,label.names],pred[,1],xlab = "Actual", ylab = "Predicted")
abline(0,(1+good),col='green', lwd = 3)
abline(0,(1-good),col='green', lwd = 3)
abline(0,(1+ok),col='blue', lwd = 3)
abline(0,(1-ok),col='blue', lwd = 3)
}Setup Formulae
n <- names(data.train)
formula <- as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~", paste(n[!n %in% label.names], collapse = " + ")))
grand.mean.formula = as.formula(paste(paste(n[n %in% label.names], collapse = " + ")," ~ 1"))
print(formula)## y3 ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10 + x11 +
## x12 + x13 + x14 + x15 + x16 + x17 + x19 + x20 + x21 + x22 +
## x23 + stat1 + stat2 + stat3 + stat4 + stat5 + stat6 + stat7 +
## stat8 + stat9 + stat10 + stat11 + stat12 + stat13 + stat14 +
## stat15 + stat16 + stat17 + stat18 + stat19 + stat20 + stat21 +
## stat22 + stat23 + stat24 + stat25 + stat26 + stat27 + stat28 +
## stat29 + stat30 + stat31 + stat32 + stat33 + stat34 + stat35 +
## stat36 + stat37 + stat38 + stat39 + stat40 + stat41 + stat42 +
## stat43 + stat44 + stat45 + stat46 + stat47 + stat48 + stat49 +
## stat50 + stat51 + stat52 + stat53 + stat54 + stat55 + stat56 +
## stat57 + stat58 + stat59 + stat60 + stat61 + stat62 + stat63 +
## stat64 + stat65 + stat66 + stat67 + stat68 + stat69 + stat70 +
## stat71 + stat72 + stat73 + stat74 + stat75 + stat76 + stat77 +
## stat78 + stat79 + stat80 + stat81 + stat82 + stat83 + stat84 +
## stat85 + stat86 + stat87 + stat88 + stat89 + stat90 + stat91 +
## stat92 + stat93 + stat94 + stat95 + stat96 + stat97 + stat98 +
## stat99 + stat100 + stat101 + stat102 + stat103 + stat104 +
## stat105 + stat106 + stat107 + stat108 + stat109 + stat110 +
## stat111 + stat112 + stat113 + stat114 + stat115 + stat116 +
## stat117 + stat118 + stat119 + stat120 + stat121 + stat122 +
## stat123 + stat124 + stat125 + stat126 + stat127 + stat128 +
## stat129 + stat130 + stat131 + stat132 + stat133 + stat134 +
## stat135 + stat136 + stat137 + stat138 + stat139 + stat140 +
## stat141 + stat142 + stat143 + stat144 + stat145 + stat146 +
## stat147 + stat148 + stat149 + stat150 + stat151 + stat152 +
## stat153 + stat154 + stat155 + stat156 + stat157 + stat158 +
## stat159 + stat160 + stat161 + stat162 + stat163 + stat164 +
## stat165 + stat166 + stat167 + stat168 + stat169 + stat170 +
## stat171 + stat172 + stat173 + stat174 + stat175 + stat176 +
## stat177 + stat178 + stat179 + stat180 + stat181 + stat182 +
## stat183 + stat184 + stat185 + stat186 + stat187 + stat188 +
## stat189 + stat190 + stat191 + stat192 + stat193 + stat194 +
## stat195 + stat196 + stat197 + stat198 + stat199 + stat200 +
## stat201 + stat202 + stat203 + stat204 + stat205 + stat206 +
## stat207 + stat208 + stat209 + stat210 + stat211 + stat212 +
## stat213 + stat214 + stat215 + stat216 + stat217 + sqrt.x18print(grand.mean.formula)## y3 ~ 1# Update feature.names because we may have transformed some features
feature.names = n[!n %in% label.names]Full & Grand Means Model
model.full = lm(formula , data.train)
summary(model.full)##
## Call:
## lm(formula = formula, data = data.train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -21.502 -6.117 -1.805 4.414 56.338
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.825e+01 2.787e+00 31.665 < 2e-16 ***
## x1 -2.320e-01 1.907e-01 -1.217 0.223747
## x2 1.667e-01 1.219e-01 1.368 0.171488
## x3 1.072e-02 3.324e-02 0.323 0.747008
## x4 -1.278e-02 2.639e-03 -4.842 1.32e-06 ***
## x5 4.903e-02 8.656e-02 0.566 0.571163
## x6 2.305e-01 1.739e-01 1.326 0.185036
## x7 3.312e+00 1.868e-01 17.728 < 2e-16 ***
## x8 1.244e-01 4.336e-02 2.868 0.004142 **
## x9 9.609e-01 9.677e-02 9.929 < 2e-16 ***
## x10 3.145e-01 9.053e-02 3.474 0.000517 ***
## x11 5.452e+07 2.167e+07 2.516 0.011905 *
## x12 -7.120e-02 5.486e-02 -1.298 0.194424
## x13 2.580e-02 2.194e-02 1.176 0.239619
## x14 -2.396e-01 9.492e-02 -2.525 0.011610 *
## x15 2.946e-02 8.993e-02 0.328 0.743203
## x16 2.764e-01 6.202e-02 4.457 8.47e-06 ***
## x17 4.480e-01 9.511e-02 4.710 2.53e-06 ***
## x19 4.363e-02 4.808e-02 0.907 0.364199
## x20 -1.396e-01 3.353e-01 -0.416 0.677155
## x21 3.960e-02 1.237e-02 3.200 0.001380 **
## x22 -1.354e-01 1.008e-01 -1.343 0.179445
## x23 4.060e-02 9.540e-02 0.426 0.670418
## stat1 3.225e-02 7.251e-02 0.445 0.656466
## stat2 8.969e-02 7.237e-02 1.239 0.215266
## stat3 1.055e-01 7.256e-02 1.454 0.146125
## stat4 -1.438e-01 7.278e-02 -1.976 0.048188 *
## stat5 -4.047e-03 7.278e-02 -0.056 0.955656
## stat6 -2.827e-02 7.240e-02 -0.390 0.696216
## stat7 -3.069e-02 7.262e-02 -0.423 0.672639
## stat8 -2.322e-03 7.276e-02 -0.032 0.974547
## stat9 -6.983e-02 7.216e-02 -0.968 0.333229
## stat10 -5.304e-02 7.274e-02 -0.729 0.465870
## stat11 -4.061e-02 7.321e-02 -0.555 0.579179
## stat12 -9.540e-03 7.243e-02 -0.132 0.895212
## stat13 -1.915e-01 7.213e-02 -2.654 0.007965 **
## stat14 -2.844e-01 7.228e-02 -3.935 8.43e-05 ***
## stat15 -8.377e-02 7.206e-02 -1.163 0.245079
## stat16 8.093e-02 7.220e-02 1.121 0.262387
## stat17 -7.472e-02 7.197e-02 -1.038 0.299163
## stat18 -6.468e-02 7.224e-02 -0.895 0.370639
## stat19 8.778e-02 7.223e-02 1.215 0.224314
## stat20 -5.830e-02 7.242e-02 -0.805 0.420830
## stat21 -5.658e-02 7.316e-02 -0.773 0.439326
## stat22 -1.109e-01 7.239e-02 -1.532 0.125598
## stat23 1.391e-01 7.201e-02 1.932 0.053417 .
## stat24 -1.521e-01 7.244e-02 -2.100 0.035748 *
## stat25 -1.725e-01 7.231e-02 -2.385 0.017091 *
## stat26 -7.795e-02 7.242e-02 -1.076 0.281788
## stat27 3.888e-02 7.250e-02 0.536 0.591786
## stat28 3.086e-02 7.241e-02 0.426 0.669990
## stat29 1.092e-01 7.260e-02 1.505 0.132442
## stat30 4.929e-02 7.285e-02 0.677 0.498704
## stat31 -7.019e-02 7.301e-02 -0.961 0.336402
## stat32 3.670e-02 7.260e-02 0.505 0.613263
## stat33 -7.833e-02 7.230e-02 -1.083 0.278702
## stat34 1.291e-02 7.260e-02 0.178 0.858906
## stat35 -8.799e-02 7.226e-02 -1.218 0.223374
## stat36 -1.414e-02 7.193e-02 -0.197 0.844209
## stat37 -9.002e-02 7.296e-02 -1.234 0.217342
## stat38 1.460e-01 7.230e-02 2.020 0.043442 *
## stat39 -1.404e-01 7.218e-02 -1.945 0.051828 .
## stat40 1.373e-02 7.281e-02 0.189 0.850437
## stat41 -1.385e-01 7.236e-02 -1.914 0.055637 .
## stat42 -6.215e-02 7.204e-02 -0.863 0.388346
## stat43 -4.051e-02 7.213e-02 -0.562 0.574430
## stat44 4.967e-02 7.236e-02 0.686 0.492436
## stat45 -1.099e-01 7.269e-02 -1.512 0.130637
## stat46 7.452e-02 7.264e-02 1.026 0.304931
## stat47 1.071e-01 7.295e-02 1.468 0.142235
## stat48 1.106e-01 7.271e-02 1.521 0.128201
## stat49 6.335e-02 7.203e-02 0.880 0.379165
## stat50 6.341e-02 7.142e-02 0.888 0.374616
## stat51 1.439e-01 7.228e-02 1.991 0.046509 *
## stat52 2.014e-03 7.243e-02 0.028 0.977813
## stat53 -6.237e-02 7.316e-02 -0.852 0.394014
## stat54 -9.075e-02 7.279e-02 -1.247 0.212565
## stat55 8.632e-02 7.175e-02 1.203 0.229001
## stat56 -4.174e-02 7.294e-02 -0.572 0.567199
## stat57 -5.133e-02 7.182e-02 -0.715 0.474808
## stat58 1.883e-02 7.151e-02 0.263 0.792276
## stat59 8.842e-02 7.247e-02 1.220 0.222512
## stat60 2.230e-01 7.282e-02 3.062 0.002209 **
## stat61 -8.237e-02 7.262e-02 -1.134 0.256711
## stat62 -8.644e-02 7.222e-02 -1.197 0.231400
## stat63 7.546e-02 7.271e-02 1.038 0.299433
## stat64 -7.450e-02 7.171e-02 -1.039 0.298892
## stat65 -1.213e-01 7.235e-02 -1.676 0.093751 .
## stat66 1.186e-01 7.290e-02 1.627 0.103734
## stat67 -5.376e-02 7.276e-02 -0.739 0.460056
## stat68 -2.551e-02 7.308e-02 -0.349 0.727020
## stat69 4.040e-03 7.249e-02 0.056 0.955559
## stat70 3.379e-02 7.192e-02 0.470 0.638484
## stat71 1.855e-02 7.212e-02 0.257 0.797057
## stat72 -2.520e-02 7.274e-02 -0.346 0.729036
## stat73 5.660e-02 7.317e-02 0.774 0.439199
## stat74 -7.429e-03 7.265e-02 -0.102 0.918557
## stat75 -7.046e-02 7.272e-02 -0.969 0.332650
## stat76 1.625e-02 7.255e-02 0.224 0.822774
## stat77 7.897e-03 7.239e-02 0.109 0.913139
## stat78 -2.606e-02 7.263e-02 -0.359 0.719750
## stat79 -2.538e-02 7.217e-02 -0.352 0.725103
## stat80 2.142e-02 7.304e-02 0.293 0.769358
## stat81 1.396e-01 7.293e-02 1.914 0.055677 .
## stat82 1.540e-02 7.238e-02 0.213 0.831534
## stat83 2.034e-02 7.231e-02 0.281 0.778529
## stat84 -3.312e-02 7.228e-02 -0.458 0.646828
## stat85 -2.204e-02 7.258e-02 -0.304 0.761409
## stat86 -1.417e-04 7.281e-02 -0.002 0.998447
## stat87 -4.484e-02 7.283e-02 -0.616 0.538168
## stat88 -8.369e-02 7.217e-02 -1.160 0.246270
## stat89 -9.484e-02 7.189e-02 -1.319 0.187135
## stat90 -4.933e-02 7.255e-02 -0.680 0.496555
## stat91 -1.033e-01 7.175e-02 -1.440 0.149947
## stat92 -9.999e-02 7.233e-02 -1.382 0.166893
## stat93 -8.119e-02 7.315e-02 -1.110 0.267101
## stat94 -6.798e-02 7.270e-02 -0.935 0.349796
## stat95 -3.186e-02 7.226e-02 -0.441 0.659325
## stat96 -1.128e-01 7.217e-02 -1.563 0.118146
## stat97 -1.971e-03 7.204e-02 -0.027 0.978172
## stat98 9.547e-01 7.108e-02 13.432 < 2e-16 ***
## stat99 7.922e-02 7.260e-02 1.091 0.275277
## stat100 1.608e-01 7.234e-02 2.224 0.026219 *
## stat101 -4.656e-02 7.290e-02 -0.639 0.523037
## stat102 3.043e-03 7.251e-02 0.042 0.966531
## stat103 -9.097e-02 7.340e-02 -1.239 0.215242
## stat104 -9.652e-02 7.247e-02 -1.332 0.182935
## stat105 1.360e-01 7.206e-02 1.887 0.059254 .
## stat106 -1.019e-01 7.248e-02 -1.406 0.159630
## stat107 -8.523e-03 7.223e-02 -0.118 0.906070
## stat108 -3.265e-02 7.271e-02 -0.449 0.653440
## stat109 5.340e-02 7.238e-02 0.738 0.460707
## stat110 -9.451e-01 7.215e-02 -13.100 < 2e-16 ***
## stat111 -4.018e-03 7.213e-02 -0.056 0.955584
## stat112 3.551e-02 7.327e-02 0.485 0.627926
## stat113 -7.316e-03 7.305e-02 -0.100 0.920230
## stat114 3.321e-02 7.230e-02 0.459 0.646042
## stat115 5.756e-02 7.217e-02 0.798 0.425153
## stat116 2.900e-02 7.306e-02 0.397 0.691392
## stat117 2.466e-02 7.293e-02 0.338 0.735317
## stat118 -7.623e-02 7.211e-02 -1.057 0.290513
## stat119 2.174e-02 7.221e-02 0.301 0.763326
## stat120 4.794e-02 7.208e-02 0.665 0.505989
## stat121 6.168e-02 7.295e-02 0.845 0.397880
## stat122 -5.506e-02 7.230e-02 -0.762 0.446360
## stat123 -1.940e-02 7.335e-02 -0.264 0.791440
## stat124 -1.505e-04 7.252e-02 -0.002 0.998345
## stat125 9.547e-02 7.254e-02 1.316 0.188210
## stat126 2.905e-02 7.195e-02 0.404 0.686370
## stat127 2.455e-02 7.238e-02 0.339 0.734493
## stat128 -6.271e-02 7.237e-02 -0.867 0.386197
## stat129 -1.232e-02 7.222e-02 -0.171 0.864545
## stat130 1.118e-01 7.255e-02 1.541 0.123273
## stat131 -6.583e-02 7.262e-02 -0.906 0.364745
## stat132 -4.165e-02 7.170e-02 -0.581 0.561320
## stat133 -3.139e-02 7.272e-02 -0.432 0.666030
## stat134 -9.479e-02 7.191e-02 -1.318 0.187466
## stat135 -4.386e-02 7.253e-02 -0.605 0.545449
## stat136 -4.759e-02 7.295e-02 -0.652 0.514160
## stat137 -2.344e-03 7.196e-02 -0.033 0.974013
## stat138 3.392e-02 7.222e-02 0.470 0.638568
## stat139 3.415e-02 7.259e-02 0.470 0.638082
## stat140 -3.790e-02 7.227e-02 -0.524 0.600050
## stat141 4.155e-02 7.185e-02 0.578 0.563147
## stat142 -1.571e-02 7.334e-02 -0.214 0.830407
## stat143 4.738e-02 7.235e-02 0.655 0.512613
## stat144 1.631e-01 7.175e-02 2.274 0.023030 *
## stat145 5.432e-02 7.343e-02 0.740 0.459485
## stat146 -1.127e-01 7.306e-02 -1.543 0.122845
## stat147 -7.466e-02 7.328e-02 -1.019 0.308273
## stat148 -2.489e-02 7.142e-02 -0.349 0.727471
## stat149 -2.118e-01 7.320e-02 -2.894 0.003821 **
## stat150 -1.225e-02 7.312e-02 -0.168 0.866955
## stat151 -1.178e-01 7.368e-02 -1.599 0.109822
## stat152 -5.257e-02 7.200e-02 -0.730 0.465337
## stat153 3.992e-02 7.354e-02 0.543 0.587255
## stat154 9.087e-02 7.303e-02 1.244 0.213473
## stat155 2.563e-02 7.243e-02 0.354 0.723402
## stat156 1.110e-01 7.313e-02 1.517 0.129250
## stat157 -2.562e-02 7.235e-02 -0.354 0.723261
## stat158 -1.937e-02 7.378e-02 -0.263 0.792897
## stat159 -1.684e-02 7.223e-02 -0.233 0.815629
## stat160 -2.547e-02 7.266e-02 -0.351 0.725951
## stat161 1.132e-02 7.296e-02 0.155 0.876709
## stat162 -6.291e-03 7.206e-02 -0.087 0.930436
## stat163 3.706e-02 7.296e-02 0.508 0.611532
## stat164 1.873e-02 7.279e-02 0.257 0.796924
## stat165 3.490e-02 7.184e-02 0.486 0.627124
## stat166 -8.238e-02 7.171e-02 -1.149 0.250734
## stat167 -7.347e-02 7.218e-02 -1.018 0.308769
## stat168 -9.786e-03 7.237e-02 -0.135 0.892435
## stat169 5.296e-02 7.284e-02 0.727 0.467232
## stat170 -7.460e-03 7.263e-02 -0.103 0.918194
## stat171 -8.802e-03 7.334e-02 -0.120 0.904478
## stat172 4.281e-02 7.189e-02 0.595 0.551577
## stat173 -6.928e-02 7.295e-02 -0.950 0.342309
## stat174 -4.757e-03 7.209e-02 -0.066 0.947385
## stat175 -9.221e-02 7.285e-02 -1.266 0.205601
## stat176 2.940e-02 7.219e-02 0.407 0.683871
## stat177 1.812e-02 7.271e-02 0.249 0.803166
## stat178 1.170e-02 7.358e-02 0.159 0.873632
## stat179 2.680e-03 7.238e-02 0.037 0.970462
## stat180 -1.081e-02 7.152e-02 -0.151 0.879889
## stat181 7.393e-03 7.291e-02 0.101 0.919240
## stat182 -1.477e-02 7.292e-02 -0.203 0.839488
## stat183 6.013e-02 7.220e-02 0.833 0.404991
## stat184 -7.518e-02 7.321e-02 -1.027 0.304517
## stat185 -3.010e-02 7.202e-02 -0.418 0.676037
## stat186 -7.498e-02 7.300e-02 -1.027 0.304392
## stat187 -6.789e-02 7.233e-02 -0.939 0.347925
## stat188 -2.282e-02 7.194e-02 -0.317 0.751106
## stat189 -2.529e-02 7.239e-02 -0.349 0.726869
## stat190 -3.252e-02 7.230e-02 -0.450 0.652849
## stat191 -1.376e-01 7.242e-02 -1.900 0.057515 .
## stat192 6.202e-02 7.317e-02 0.848 0.396645
## stat193 -9.605e-03 7.320e-02 -0.131 0.895602
## stat194 2.088e-02 7.218e-02 0.289 0.772352
## stat195 1.419e-01 7.208e-02 1.969 0.049052 *
## stat196 -3.608e-02 7.328e-02 -0.492 0.622511
## stat197 -1.957e-02 7.164e-02 -0.273 0.784734
## stat198 -1.161e-01 7.256e-02 -1.600 0.109709
## stat199 1.039e-01 7.195e-02 1.444 0.148845
## stat200 -1.090e-01 7.182e-02 -1.518 0.129078
## stat201 -2.455e-02 7.249e-02 -0.339 0.734847
## stat202 -9.994e-02 7.333e-02 -1.363 0.172961
## stat203 9.070e-03 7.202e-02 0.126 0.899777
## stat204 -1.423e-01 7.233e-02 -1.968 0.049114 *
## stat205 -1.376e-01 7.214e-02 -1.907 0.056589 .
## stat206 -6.280e-02 7.248e-02 -0.866 0.386283
## stat207 7.971e-02 7.248e-02 1.100 0.271506
## stat208 -9.804e-03 7.265e-02 -0.135 0.892656
## stat209 -4.080e-02 7.222e-02 -0.565 0.572131
## stat210 -5.939e-02 7.262e-02 -0.818 0.413467
## stat211 -5.413e-02 7.241e-02 -0.748 0.454754
## stat212 2.444e-02 7.240e-02 0.338 0.735664
## stat213 -1.069e-02 7.307e-02 -0.146 0.883671
## stat214 -1.517e-01 7.216e-02 -2.102 0.035565 *
## stat215 -9.782e-02 7.282e-02 -1.343 0.179246
## stat216 -3.596e-02 7.262e-02 -0.495 0.620439
## stat217 1.334e-01 7.258e-02 1.838 0.066079 .
## sqrt.x18 7.672e+00 2.747e-01 27.929 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.527 on 5761 degrees of freedom
## Multiple R-squared: 0.2532, Adjusted R-squared: 0.2221
## F-statistic: 8.138 on 240 and 5761 DF, p-value: < 2.2e-16cd.full = plot.diagnostics(model.full, data.train)
## [1] "Number of data points that have Cook's D > 4/n: 290"
## [1] "Number of data points that have Cook's D > 1: 0"Checking with removal of high influence points
high.cd = names(cd.full[cd.full > 4/nrow(data.train)])
data.train2 = data.train[!(rownames(data.train)) %in% high.cd,]
model.full2 = lm(formula , data.train2)
summary(model.full2)##
## Call:
## lm(formula = formula, data = data.train2)
##
## Residuals:
## Min 1Q Median 3Q Max
## -18.275 -5.058 -1.015 4.618 21.568
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.627e+01 2.207e+00 39.083 < 2e-16 ***
## x1 -1.808e-01 1.513e-01 -1.195 0.232269
## x2 1.376e-01 9.646e-02 1.426 0.153805
## x3 2.865e-03 2.626e-02 0.109 0.913139
## x4 -1.452e-02 2.092e-03 -6.941 4.36e-12 ***
## x5 8.107e-02 6.853e-02 1.183 0.236886
## x6 1.003e-01 1.376e-01 0.729 0.465809
## x7 3.397e+00 1.479e-01 22.967 < 2e-16 ***
## x8 1.401e-01 3.440e-02 4.071 4.75e-05 ***
## x9 9.279e-01 7.639e-02 12.147 < 2e-16 ***
## x10 4.264e-01 7.188e-02 5.932 3.17e-09 ***
## x11 5.693e+07 1.716e+07 3.318 0.000911 ***
## x12 -5.983e-02 4.336e-02 -1.380 0.167748
## x13 3.932e-02 1.742e-02 2.258 0.024010 *
## x14 -8.512e-02 7.510e-02 -1.133 0.257098
## x15 2.541e-02 7.126e-02 0.357 0.721395
## x16 2.484e-01 4.917e-02 5.052 4.51e-07 ***
## x17 4.312e-01 7.531e-02 5.726 1.08e-08 ***
## x19 4.512e-02 3.812e-02 1.184 0.236584
## x20 -8.789e-02 2.659e-01 -0.330 0.741058
## x21 3.850e-02 9.797e-03 3.930 8.59e-05 ***
## x22 -1.651e-01 7.972e-02 -2.071 0.038440 *
## x23 8.793e-02 7.566e-02 1.162 0.245216
## stat1 -5.557e-03 5.738e-02 -0.097 0.922853
## stat2 1.152e-01 5.727e-02 2.012 0.044250 *
## stat3 1.232e-01 5.745e-02 2.145 0.031974 *
## stat4 -1.410e-01 5.780e-02 -2.440 0.014707 *
## stat5 2.594e-03 5.773e-02 0.045 0.964162
## stat6 -5.634e-02 5.732e-02 -0.983 0.325711
## stat7 -8.444e-02 5.733e-02 -1.473 0.140825
## stat8 -3.210e-02 5.759e-02 -0.557 0.577331
## stat9 -4.814e-02 5.720e-02 -0.842 0.400096
## stat10 -2.967e-02 5.752e-02 -0.516 0.605956
## stat11 -9.349e-02 5.799e-02 -1.612 0.107002
## stat12 -1.870e-02 5.732e-02 -0.326 0.744285
## stat13 -1.835e-01 5.706e-02 -3.216 0.001306 **
## stat14 -3.333e-01 5.716e-02 -5.831 5.82e-09 ***
## stat15 -1.303e-01 5.710e-02 -2.281 0.022572 *
## stat16 7.715e-03 5.707e-02 0.135 0.892474
## stat17 -3.450e-02 5.707e-02 -0.605 0.545479
## stat18 -4.885e-02 5.711e-02 -0.855 0.392427
## stat19 2.238e-02 5.733e-02 0.390 0.696301
## stat20 7.403e-04 5.738e-02 0.013 0.989707
## stat21 -5.914e-02 5.796e-02 -1.020 0.307595
## stat22 -5.690e-02 5.721e-02 -0.994 0.320025
## stat23 1.934e-01 5.711e-02 3.387 0.000711 ***
## stat24 -1.190e-01 5.738e-02 -2.075 0.038062 *
## stat25 -1.657e-01 5.720e-02 -2.896 0.003792 **
## stat26 -9.415e-02 5.743e-02 -1.639 0.101175
## stat27 3.320e-02 5.753e-02 0.577 0.563933
## stat28 -2.306e-03 5.735e-02 -0.040 0.967928
## stat29 5.450e-02 5.747e-02 0.948 0.342970
## stat30 2.852e-02 5.751e-02 0.496 0.620012
## stat31 -2.857e-02 5.775e-02 -0.495 0.620799
## stat32 9.192e-03 5.748e-02 0.160 0.872968
## stat33 -7.215e-02 5.726e-02 -1.260 0.207739
## stat34 6.166e-02 5.741e-02 1.074 0.282792
## stat35 -1.004e-01 5.724e-02 -1.754 0.079403 .
## stat36 -3.296e-02 5.711e-02 -0.577 0.563914
## stat37 -4.599e-02 5.780e-02 -0.796 0.426233
## stat38 1.493e-01 5.704e-02 2.617 0.008896 **
## stat39 -1.509e-01 5.715e-02 -2.641 0.008286 **
## stat40 -2.150e-02 5.769e-02 -0.373 0.709364
## stat41 -1.685e-01 5.721e-02 -2.945 0.003248 **
## stat42 -5.188e-02 5.708e-02 -0.909 0.363425
## stat43 -7.581e-02 5.704e-02 -1.329 0.183828
## stat44 2.881e-02 5.738e-02 0.502 0.615649
## stat45 -1.036e-01 5.760e-02 -1.798 0.072188 .
## stat46 7.042e-02 5.749e-02 1.225 0.220607
## stat47 9.264e-02 5.775e-02 1.604 0.108725
## stat48 9.483e-02 5.738e-02 1.653 0.098467 .
## stat49 1.870e-02 5.703e-02 0.328 0.742957
## stat50 9.248e-02 5.661e-02 1.633 0.102424
## stat51 9.265e-02 5.727e-02 1.618 0.105743
## stat52 5.429e-02 5.746e-02 0.945 0.344844
## stat53 -8.941e-02 5.795e-02 -1.543 0.122908
## stat54 -1.230e-01 5.779e-02 -2.128 0.033376 *
## stat55 9.500e-02 5.694e-02 1.668 0.095325 .
## stat56 8.579e-03 5.771e-02 0.149 0.881822
## stat57 -4.550e-02 5.700e-02 -0.798 0.424773
## stat58 -1.330e-02 5.657e-02 -0.235 0.814165
## stat59 8.249e-02 5.740e-02 1.437 0.150740
## stat60 2.279e-01 5.770e-02 3.950 7.91e-05 ***
## stat61 -1.024e-01 5.739e-02 -1.783 0.074566 .
## stat62 -8.550e-02 5.709e-02 -1.498 0.134260
## stat63 5.465e-02 5.769e-02 0.947 0.343588
## stat64 1.903e-02 5.678e-02 0.335 0.737509
## stat65 -7.236e-02 5.723e-02 -1.264 0.206194
## stat66 5.825e-02 5.773e-02 1.009 0.312985
## stat67 2.151e-02 5.761e-02 0.373 0.708863
## stat68 -3.366e-02 5.787e-02 -0.582 0.560868
## stat69 -3.735e-02 5.749e-02 -0.650 0.515897
## stat70 2.902e-02 5.696e-02 0.509 0.610433
## stat71 4.596e-02 5.724e-02 0.803 0.421978
## stat72 -4.214e-02 5.757e-02 -0.732 0.464223
## stat73 6.503e-02 5.798e-02 1.122 0.262063
## stat74 2.143e-02 5.759e-02 0.372 0.709816
## stat75 1.930e-03 5.754e-02 0.034 0.973240
## stat76 1.520e-02 5.737e-02 0.265 0.791120
## stat77 7.852e-02 5.735e-02 1.369 0.171004
## stat78 -7.465e-02 5.739e-02 -1.301 0.193408
## stat79 3.755e-02 5.708e-02 0.658 0.510649
## stat80 5.460e-02 5.786e-02 0.944 0.345409
## stat81 7.481e-02 5.775e-02 1.295 0.195236
## stat82 1.219e-02 5.727e-02 0.213 0.831417
## stat83 -1.067e-02 5.717e-02 -0.187 0.851965
## stat84 -5.365e-02 5.722e-02 -0.937 0.348560
## stat85 -1.322e-01 5.750e-02 -2.298 0.021571 *
## stat86 1.507e-02 5.767e-02 0.261 0.793921
## stat87 -4.472e-02 5.769e-02 -0.775 0.438277
## stat88 -4.215e-02 5.725e-02 -0.736 0.461664
## stat89 -5.042e-02 5.707e-02 -0.883 0.377022
## stat90 -3.843e-02 5.746e-02 -0.669 0.503592
## stat91 -1.144e-01 5.672e-02 -2.017 0.043743 *
## stat92 -6.060e-02 5.723e-02 -1.059 0.289731
## stat93 -2.720e-02 5.814e-02 -0.468 0.639924
## stat94 -9.964e-03 5.747e-02 -0.173 0.862350
## stat95 4.884e-02 5.732e-02 0.852 0.394184
## stat96 -1.285e-01 5.719e-02 -2.247 0.024683 *
## stat97 -3.886e-03 5.704e-02 -0.068 0.945678
## stat98 8.773e-01 5.629e-02 15.584 < 2e-16 ***
## stat99 9.186e-02 5.749e-02 1.598 0.110143
## stat100 1.657e-01 5.735e-02 2.889 0.003884 **
## stat101 2.713e-02 5.777e-02 0.470 0.638690
## stat102 -4.829e-03 5.744e-02 -0.084 0.933009
## stat103 -1.021e-01 5.799e-02 -1.761 0.078222 .
## stat104 -3.410e-02 5.743e-02 -0.594 0.552720
## stat105 1.010e-01 5.713e-02 1.768 0.077185 .
## stat106 -1.248e-01 5.730e-02 -2.178 0.029451 *
## stat107 1.552e-02 5.719e-02 0.271 0.786133
## stat108 1.579e-02 5.771e-02 0.274 0.784413
## stat109 1.877e-02 5.738e-02 0.327 0.743593
## stat110 -9.104e-01 5.689e-02 -16.003 < 2e-16 ***
## stat111 4.295e-02 5.700e-02 0.754 0.451119
## stat112 2.393e-02 5.815e-02 0.412 0.680720
## stat113 4.438e-02 5.777e-02 0.768 0.442406
## stat114 5.291e-02 5.735e-02 0.923 0.356260
## stat115 8.263e-02 5.712e-02 1.447 0.148039
## stat116 1.154e-02 5.783e-02 0.200 0.841848
## stat117 2.816e-02 5.762e-02 0.489 0.625089
## stat118 -2.938e-03 5.706e-02 -0.051 0.958944
## stat119 9.468e-02 5.707e-02 1.659 0.097147 .
## stat120 -3.730e-02 5.706e-02 -0.654 0.513304
## stat121 3.962e-02 5.770e-02 0.687 0.492325
## stat122 -6.359e-02 5.731e-02 -1.110 0.267233
## stat123 3.142e-02 5.799e-02 0.542 0.587974
## stat124 -4.830e-02 5.737e-02 -0.842 0.399888
## stat125 2.816e-02 5.747e-02 0.490 0.624103
## stat126 1.290e-02 5.698e-02 0.226 0.820865
## stat127 -3.125e-02 5.731e-02 -0.545 0.585555
## stat128 -1.396e-01 5.721e-02 -2.440 0.014721 *
## stat129 -1.417e-02 5.714e-02 -0.248 0.804114
## stat130 1.154e-01 5.739e-02 2.010 0.044454 *
## stat131 -5.255e-02 5.746e-02 -0.915 0.360455
## stat132 -8.327e-02 5.682e-02 -1.465 0.142850
## stat133 2.781e-02 5.771e-02 0.482 0.629832
## stat134 -3.907e-02 5.693e-02 -0.686 0.492541
## stat135 -5.797e-02 5.746e-02 -1.009 0.313125
## stat136 -6.661e-02 5.782e-02 -1.152 0.249365
## stat137 6.565e-02 5.686e-02 1.155 0.248329
## stat138 -1.572e-02 5.708e-02 -0.275 0.782951
## stat139 2.911e-02 5.750e-02 0.506 0.612715
## stat140 -1.775e-02 5.708e-02 -0.311 0.755764
## stat141 6.151e-02 5.687e-02 1.082 0.279516
## stat142 2.939e-02 5.810e-02 0.506 0.612940
## stat143 1.486e-02 5.723e-02 0.260 0.795126
## stat144 1.481e-01 5.680e-02 2.607 0.009167 **
## stat145 5.317e-02 5.832e-02 0.912 0.361909
## stat146 -1.289e-01 5.786e-02 -2.228 0.025942 *
## stat147 -5.193e-02 5.813e-02 -0.893 0.371700
## stat148 -2.531e-02 5.664e-02 -0.447 0.654998
## stat149 -1.977e-01 5.807e-02 -3.404 0.000668 ***
## stat150 -2.637e-02 5.800e-02 -0.455 0.649356
## stat151 7.341e-03 5.848e-02 0.126 0.900106
## stat152 -2.164e-02 5.694e-02 -0.380 0.703868
## stat153 4.985e-02 5.813e-02 0.858 0.391170
## stat154 8.882e-02 5.786e-02 1.535 0.124849
## stat155 6.200e-02 5.744e-02 1.079 0.280515
## stat156 7.208e-02 5.782e-02 1.247 0.212571
## stat157 -2.530e-02 5.728e-02 -0.442 0.658687
## stat158 5.211e-02 5.840e-02 0.892 0.372257
## stat159 1.792e-02 5.725e-02 0.313 0.754245
## stat160 3.344e-05 5.764e-02 0.001 0.999537
## stat161 1.597e-02 5.776e-02 0.277 0.782156
## stat162 -1.096e-02 5.697e-02 -0.192 0.847435
## stat163 3.388e-02 5.791e-02 0.585 0.558579
## stat164 -3.465e-03 5.770e-02 -0.060 0.952112
## stat165 4.378e-02 5.693e-02 0.769 0.441876
## stat166 -4.773e-02 5.670e-02 -0.842 0.399934
## stat167 -1.066e-01 5.718e-02 -1.865 0.062219 .
## stat168 -2.203e-02 5.720e-02 -0.385 0.700100
## stat169 3.950e-02 5.777e-02 0.684 0.494191
## stat170 1.655e-02 5.749e-02 0.288 0.773499
## stat171 -6.160e-02 5.809e-02 -1.060 0.288972
## stat172 1.207e-01 5.683e-02 2.124 0.033712 *
## stat173 -3.574e-02 5.781e-02 -0.618 0.536423
## stat174 3.174e-02 5.706e-02 0.556 0.578108
## stat175 -7.213e-02 5.755e-02 -1.253 0.210093
## stat176 -4.151e-02 5.719e-02 -0.726 0.467970
## stat177 -1.082e-01 5.761e-02 -1.879 0.060306 .
## stat178 1.797e-02 5.830e-02 0.308 0.757906
## stat179 3.178e-02 5.729e-02 0.555 0.579083
## stat180 3.506e-02 5.674e-02 0.618 0.536667
## stat181 3.230e-02 5.761e-02 0.561 0.575045
## stat182 5.589e-02 5.779e-02 0.967 0.333519
## stat183 4.603e-02 5.722e-02 0.804 0.421254
## stat184 -7.994e-03 5.791e-02 -0.138 0.890205
## stat185 1.261e-02 5.715e-02 0.221 0.825358
## stat186 1.683e-02 5.783e-02 0.291 0.771062
## stat187 -4.205e-02 5.711e-02 -0.736 0.461587
## stat188 -1.243e-02 5.708e-02 -0.218 0.827639
## stat189 -7.784e-02 5.742e-02 -1.355 0.175335
## stat190 -8.823e-02 5.723e-02 -1.542 0.123204
## stat191 -9.211e-02 5.730e-02 -1.607 0.108009
## stat192 1.026e-02 5.796e-02 0.177 0.859524
## stat193 5.146e-02 5.802e-02 0.887 0.375108
## stat194 -4.512e-02 5.723e-02 -0.788 0.430486
## stat195 2.419e-02 5.718e-02 0.423 0.672307
## stat196 -2.180e-02 5.796e-02 -0.376 0.706896
## stat197 -4.581e-02 5.672e-02 -0.808 0.419272
## stat198 -8.382e-02 5.739e-02 -1.460 0.144220
## stat199 5.015e-02 5.697e-02 0.880 0.378713
## stat200 -1.498e-02 5.696e-02 -0.263 0.792615
## stat201 -2.924e-02 5.760e-02 -0.508 0.611696
## stat202 -4.623e-02 5.818e-02 -0.795 0.426843
## stat203 3.230e-02 5.698e-02 0.567 0.570863
## stat204 -6.816e-02 5.728e-02 -1.190 0.234098
## stat205 -2.033e-02 5.696e-02 -0.357 0.721245
## stat206 -1.062e-01 5.737e-02 -1.852 0.064136 .
## stat207 9.038e-02 5.736e-02 1.576 0.115175
## stat208 3.438e-02 5.758e-02 0.597 0.550506
## stat209 1.609e-03 5.710e-02 0.028 0.977516
## stat210 -6.548e-02 5.748e-02 -1.139 0.254675
## stat211 -3.862e-02 5.730e-02 -0.674 0.500268
## stat212 4.936e-02 5.731e-02 0.861 0.389135
## stat213 2.916e-02 5.772e-02 0.505 0.613450
## stat214 -1.051e-01 5.720e-02 -1.838 0.066121 .
## stat215 -8.115e-02 5.775e-02 -1.405 0.160041
## stat216 -4.982e-02 5.733e-02 -0.869 0.384922
## stat217 7.288e-02 5.754e-02 1.266 0.205398
## sqrt.x18 7.547e+00 2.169e-01 34.796 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.351 on 5471 degrees of freedom
## Multiple R-squared: 0.3562, Adjusted R-squared: 0.328
## F-statistic: 12.61 on 240 and 5471 DF, p-value: < 2.2e-16cd.full2 = plot.diagnostics(model.full2, data.train2)
## [1] "Number of data points that have Cook's D > 4/n: 315"
## [1] "Number of data points that have Cook's D > 1: 0"# much more normal residuals than before.
# See if you can check the distribution (boxplots) of the high leverage points and the other points
# High Leverage Plot MMORO ###
cd.compare = data.frame(cd = cd.full) %>% mutate(type = ifelse(cd > 4/nrow(data.train),'High','Normal'))
ggplot(data=cd.compare, aes(x=type,y=cd)) +
geom_boxplot(fill='light blue') +
scale_y_continuous(trans='log',name="Cook's Distance (log)") +
theme_light() +
ggtitle('Distribution of High Leverage Points and Normal Points')
model.null = lm(grand.mean.formula, data.train)
# summary(model.null)
# plot.diagnostics(model.null, data.train)model.null2 = lm(grand.mean.formula, data.train2)
# summary(model.null2)
# plot.diagnostics(model.null2, data.train2)Variable Selection
Basic: http://www.stat.columbia.edu/~martin/W2024/R10.pdf Cross Validation + Other Metrics: http://www.sthda.com/english/articles/37-model-selection-essentials-in-r/154-stepwise-regression-essentials-in-r/
Forward Selection (w/ full train)
Train
if (algo.forward == TRUE){
t1 = Sys.time()
model.forward = step(model.null, scope=list(lower=model.null, upper=model.full), direction="forward", trace = 0)
print(summary(model.forward))
#saveRDS(model.forward,file = "model_forward.rds")
t2 = Sys.time()
print (paste("Time taken for Forward Selection: ",t2-t1, sep = ""))
plot.diagnostics(model.forward, data.train)
}Test
if (algo.forward == TRUE){
test.model(model.forward, data.test, "Forward Selection")
}Forward Selection (w/ filtered train)
Train
if (algo.forward == TRUE){
t1 = Sys.time()
model.forward2 = step(model.null2, scope=list(lower=model.null2, upper=model.full2), direction="forward", trace = 0)
print(summary(model.forward2))
#saveRDS(model.forward,file = "model_forward.rds")
t2 = Sys.time()
print (paste("Time taken for Forward Selection: ",t2-t1, sep = ""))
plot.diagnostics(model.forward2, data.train2)
}Test
if (algo.forward == TRUE){
test.model(model.forward2, data.test, "Forward Selection (2)")
}Forward Selection with CV (w/ full train)
Train
if (algo.forward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
, data = data.train
, method = "leapForward"
, feature.names = feature.names)
model.forward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 16 on full training set
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 10.205848 0.1070230 7.793298 0.4837937 0.02121144 0.2343155
## 2 2 9.978578 0.1456242 7.594919 0.4865059 0.01542500 0.2210630
## 3 3 9.869319 0.1645156 7.472217 0.4757917 0.01700325 0.2032220
## 4 4 9.705345 0.1918124 7.255723 0.4773872 0.01219753 0.1920870
## 5 5 9.623121 0.2056678 7.191041 0.5001426 0.01530975 0.2093101
## 6 6 9.615614 0.2067906 7.190418 0.4962592 0.01340840 0.1969631
## 7 7 9.599094 0.2094876 7.178668 0.4953228 0.01391436 0.2006617
## 8 8 9.581185 0.2124654 7.171670 0.4983385 0.01423833 0.2054035
## 9 9 9.573978 0.2136032 7.160477 0.4946051 0.01182847 0.1967355
## 10 10 9.566457 0.2148079 7.156153 0.4890367 0.01057451 0.1936818
## 11 11 9.567690 0.2147292 7.159764 0.4979287 0.01271238 0.2087616
## 12 12 9.570734 0.2142485 7.161341 0.4950334 0.01178461 0.2061083
## 13 13 9.569555 0.2144817 7.158617 0.4954577 0.01207316 0.2005056
## 14 14 9.569202 0.2145821 7.160108 0.4886390 0.01088688 0.1991866
## 15 15 9.568774 0.2146047 7.157827 0.4818420 0.01068948 0.1909961
## 16 16 9.565261 0.2152305 7.160380 0.4895184 0.01216199 0.1976081
## 17 17 9.567334 0.2149625 7.164737 0.4913768 0.01360563 0.2009011
## 18 18 9.572223 0.2142536 7.165375 0.4935820 0.01405113 0.2001792
## 19 19 9.567220 0.2151634 7.160656 0.4986940 0.01458215 0.2066717
## 20 20 9.571368 0.2145047 7.164174 0.4933182 0.01386590 0.1989496
## 21 21 9.567416 0.2152074 7.159803 0.4941473 0.01404452 0.2018575
## 22 22 9.571406 0.2145969 7.160732 0.4957266 0.01458413 0.2060193
## 23 23 9.575425 0.2139530 7.161713 0.4970140 0.01432900 0.2056816
## 24 24 9.584611 0.2125175 7.168373 0.4956858 0.01421770 0.2002674
## 25 25 9.581901 0.2129427 7.164419 0.4953870 0.01386644 0.1996005
## 26 26 9.583743 0.2127369 7.164793 0.4979161 0.01452431 0.1991570
## 27 27 9.584930 0.2125648 7.166746 0.4946890 0.01388254 0.1933937
## 28 28 9.592303 0.2114755 7.176218 0.4955237 0.01422260 0.1955142
## 29 29 9.594619 0.2111496 7.179263 0.4920210 0.01387720 0.1935187
## 30 30 9.594531 0.2111348 7.181164 0.4886627 0.01374159 0.1944880
## 31 31 9.592214 0.2115019 7.182320 0.4913554 0.01399652 0.1977549
## 32 32 9.596338 0.2108660 7.185186 0.4911173 0.01369816 0.1935786
## 33 33 9.600163 0.2102227 7.185724 0.4825230 0.01295648 0.1864999
## 34 34 9.606077 0.2093563 7.191567 0.4785715 0.01308893 0.1858295
## 35 35 9.612094 0.2084842 7.196839 0.4810674 0.01325224 0.1876467
## 36 36 9.613614 0.2082737 7.198500 0.4810632 0.01301752 0.1870024
## 37 37 9.619007 0.2073933 7.204556 0.4829169 0.01295590 0.1874158
## 38 38 9.620767 0.2071515 7.202086 0.4817776 0.01275396 0.1845823
## 39 39 9.624027 0.2066601 7.202826 0.4837002 0.01330190 0.1858999
## 40 40 9.627022 0.2061970 7.207216 0.4863355 0.01303468 0.1883853
## 41 41 9.632032 0.2054544 7.212336 0.4889318 0.01266462 0.1930146
## 42 42 9.630941 0.2056589 7.212233 0.4931403 0.01329216 0.1964734
## 43 43 9.633113 0.2053342 7.213706 0.4938240 0.01358561 0.2015098
## 44 44 9.636211 0.2049000 7.216841 0.4919803 0.01379320 0.1993277
## 45 45 9.636226 0.2049692 7.214656 0.4913235 0.01389670 0.1957690
## 46 46 9.635844 0.2050912 7.215415 0.4933396 0.01406488 0.1980321
## 47 47 9.633604 0.2054201 7.214172 0.4906287 0.01319585 0.1959893
## 48 48 9.637044 0.2049228 7.219410 0.4913375 0.01316567 0.1964193
## 49 49 9.638142 0.2047848 7.221109 0.4911534 0.01357937 0.1967339
## 50 50 9.639763 0.2045427 7.226550 0.4889001 0.01275524 0.1941188
## 51 51 9.642162 0.2041790 7.231294 0.4897592 0.01275260 0.1914550
## 52 52 9.641711 0.2042536 7.229422 0.4893983 0.01268386 0.1929917
## 53 53 9.646684 0.2035512 7.233248 0.4878977 0.01261278 0.1911499
## 54 54 9.648677 0.2033129 7.235829 0.4883934 0.01266993 0.1927885
## 55 55 9.649797 0.2032089 7.236751 0.4890812 0.01229942 0.1922051
## 56 56 9.651188 0.2030487 7.236308 0.4899266 0.01193685 0.1968934
## 57 57 9.650155 0.2032218 7.235055 0.4903257 0.01211339 0.1973277
## 58 58 9.651303 0.2030737 7.236970 0.4906843 0.01232721 0.1963263
## 59 59 9.654182 0.2026424 7.240821 0.4903826 0.01262102 0.1945804
## 60 60 9.654436 0.2025888 7.239809 0.4903490 0.01308315 0.1950564
## 61 61 9.655319 0.2024802 7.241536 0.4892310 0.01286149 0.1925803
## 62 62 9.654714 0.2025961 7.241085 0.4848763 0.01242700 0.1899459
## 63 63 9.656846 0.2023799 7.242004 0.4865223 0.01273801 0.1908949
## 64 64 9.655101 0.2026612 7.240344 0.4871345 0.01221387 0.1904239
## 65 65 9.656155 0.2025409 7.241273 0.4902918 0.01263194 0.1955224
## 66 66 9.660475 0.2019115 7.244422 0.4882990 0.01266130 0.1922495
## 67 67 9.656662 0.2024549 7.244949 0.4887937 0.01270361 0.1939563
## 68 68 9.658058 0.2022737 7.246564 0.4883509 0.01328513 0.1921142
## 69 69 9.658922 0.2021702 7.248110 0.4905271 0.01372876 0.1955497
## 70 70 9.659542 0.2021113 7.248301 0.4886902 0.01370104 0.1963318
## 71 71 9.658347 0.2023341 7.244360 0.4876363 0.01367430 0.1975858
## 72 72 9.658854 0.2022483 7.243764 0.4886420 0.01369566 0.1974729
## 73 73 9.661497 0.2018938 7.244700 0.4888370 0.01326187 0.1966830
## 74 74 9.656529 0.2026026 7.239153 0.4878159 0.01275733 0.1953722
## 75 75 9.658702 0.2022754 7.240874 0.4851514 0.01277234 0.1918310
## 76 76 9.658091 0.2024022 7.241545 0.4828952 0.01258510 0.1915073
## 77 77 9.655939 0.2027067 7.240276 0.4838051 0.01258347 0.1928427
## 78 78 9.658048 0.2024226 7.244550 0.4850144 0.01280357 0.1943126
## 79 79 9.657404 0.2025575 7.244784 0.4850124 0.01267238 0.1951341
## 80 80 9.658427 0.2024254 7.244542 0.4836787 0.01247573 0.1923515
## 81 81 9.659485 0.2023244 7.246252 0.4828629 0.01259742 0.1928354
## 82 82 9.660974 0.2021109 7.247485 0.4818481 0.01230595 0.1902835
## 83 83 9.658704 0.2025003 7.247328 0.4819665 0.01251089 0.1905502
## 84 84 9.657530 0.2026847 7.246283 0.4795291 0.01229216 0.1889392
## 85 85 9.659587 0.2023891 7.248562 0.4810647 0.01256484 0.1897930
## 86 86 9.664186 0.2017050 7.251962 0.4828956 0.01264515 0.1909245
## 87 87 9.662354 0.2019939 7.249820 0.4852275 0.01263981 0.1927229
## 88 88 9.663933 0.2017990 7.249499 0.4863098 0.01247501 0.1910270
## 89 89 9.662939 0.2019802 7.247378 0.4860883 0.01251219 0.1895289
## 90 90 9.665734 0.2015829 7.248549 0.4835262 0.01263055 0.1871058
## 91 91 9.665991 0.2015795 7.248873 0.4840365 0.01266325 0.1875797
## 92 92 9.667505 0.2013788 7.248042 0.4849326 0.01283964 0.1887931
## 93 93 9.665950 0.2016564 7.247423 0.4820112 0.01261444 0.1857881
## 94 94 9.666648 0.2015315 7.247609 0.4796665 0.01236112 0.1836397
## 95 95 9.666133 0.2016188 7.248163 0.4795595 0.01252299 0.1828430
## 96 96 9.668508 0.2012795 7.251699 0.4809960 0.01250488 0.1853130
## 97 97 9.667582 0.2014083 7.251545 0.4842224 0.01299776 0.1889252
## 98 98 9.670011 0.2010712 7.253864 0.4832461 0.01317296 0.1888060
## 99 99 9.670709 0.2009780 7.253636 0.4816196 0.01319313 0.1874263
## 100 100 9.670032 0.2010958 7.255351 0.4828631 0.01338294 0.1879891
## 101 101 9.673368 0.2006481 7.258961 0.4838703 0.01359388 0.1888615
## 102 102 9.676628 0.2002329 7.262479 0.4833262 0.01358822 0.1876588
## 103 103 9.678442 0.1999516 7.264204 0.4830861 0.01347677 0.1887335
## 104 104 9.678857 0.1998833 7.267099 0.4806289 0.01321732 0.1862020
## 105 105 9.678470 0.1999348 7.266876 0.4769057 0.01264238 0.1824511
## 106 106 9.677522 0.2000656 7.266291 0.4771336 0.01277846 0.1808448
## 107 107 9.679411 0.1997908 7.267970 0.4781202 0.01294369 0.1801825
## 108 108 9.680187 0.1996561 7.268273 0.4764454 0.01276116 0.1778914
## 109 109 9.682271 0.1993993 7.269039 0.4767379 0.01301340 0.1775527
## 110 110 9.681587 0.1995298 7.267626 0.4751738 0.01273248 0.1747409
## 111 111 9.682310 0.1994146 7.268503 0.4769211 0.01251937 0.1772595
## 112 112 9.684076 0.1991975 7.269887 0.4754739 0.01266979 0.1779162
## 113 113 9.683787 0.1992225 7.269759 0.4743589 0.01250701 0.1774515
## 114 114 9.685420 0.1990001 7.271673 0.4741482 0.01259184 0.1779413
## 115 115 9.684459 0.1991474 7.270257 0.4752595 0.01245610 0.1783746
## 116 116 9.683876 0.1992460 7.270317 0.4752343 0.01246474 0.1779957
## 117 117 9.684572 0.1991471 7.270459 0.4732485 0.01261324 0.1777548
## 118 118 9.686065 0.1989184 7.271384 0.4727663 0.01269869 0.1763239
## 119 119 9.687825 0.1986458 7.272408 0.4749034 0.01302683 0.1784585
## 120 120 9.689031 0.1984676 7.273898 0.4764223 0.01290701 0.1802110
## 121 121 9.690871 0.1982483 7.273887 0.4787129 0.01316292 0.1824292
## 122 122 9.690315 0.1983093 7.273085 0.4776322 0.01301405 0.1821575
## 123 123 9.690915 0.1982285 7.273856 0.4776575 0.01331210 0.1829433
## 124 124 9.692273 0.1980551 7.275009 0.4773972 0.01334720 0.1841497
## 125 125 9.691021 0.1982659 7.274540 0.4774782 0.01356103 0.1844282
## 126 126 9.693829 0.1978817 7.276602 0.4777448 0.01349207 0.1854113
## 127 127 9.696093 0.1975454 7.278360 0.4779849 0.01378271 0.1861958
## 128 128 9.695391 0.1976704 7.277285 0.4775272 0.01362427 0.1851510
## 129 129 9.695221 0.1976701 7.278227 0.4771897 0.01368229 0.1858387
## 130 130 9.698052 0.1972581 7.280975 0.4758814 0.01380211 0.1867169
## 131 131 9.697932 0.1973080 7.280105 0.4743183 0.01359515 0.1844420
## 132 132 9.697573 0.1973759 7.278926 0.4728649 0.01342714 0.1831860
## 133 133 9.697401 0.1973846 7.278906 0.4743068 0.01342933 0.1839856
## 134 134 9.696910 0.1974778 7.278286 0.4742292 0.01338273 0.1844546
## 135 135 9.696959 0.1974661 7.277495 0.4732000 0.01311714 0.1825098
## 136 136 9.696925 0.1974640 7.278216 0.4724719 0.01304968 0.1810694
## 137 137 9.696888 0.1974505 7.278334 0.4705115 0.01298777 0.1795606
## 138 138 9.698302 0.1972522 7.279494 0.4695786 0.01270430 0.1787285
## 139 139 9.697894 0.1973415 7.278851 0.4684540 0.01247315 0.1792546
## 140 140 9.698647 0.1972284 7.278525 0.4709878 0.01265352 0.1810533
## 141 141 9.699028 0.1971678 7.279616 0.4699891 0.01258795 0.1782861
## 142 142 9.697721 0.1973756 7.278144 0.4709476 0.01278080 0.1809148
## 143 143 9.697813 0.1973763 7.279461 0.4701423 0.01295181 0.1813189
## 144 144 9.696320 0.1975989 7.278016 0.4717822 0.01293533 0.1828000
## 145 145 9.697164 0.1974823 7.279735 0.4724538 0.01291581 0.1839452
## 146 146 9.696757 0.1975319 7.279894 0.4727043 0.01301269 0.1839774
## 147 147 9.697522 0.1974233 7.280359 0.4743347 0.01311919 0.1839354
## 148 148 9.697810 0.1973641 7.280714 0.4752357 0.01311869 0.1835338
## 149 149 9.698719 0.1972338 7.280051 0.4754688 0.01315388 0.1836875
## 150 150 9.699335 0.1971567 7.280477 0.4742080 0.01306974 0.1812704
## 151 151 9.699759 0.1971078 7.280959 0.4746626 0.01308819 0.1809339
## 152 152 9.699998 0.1970823 7.280026 0.4743606 0.01313730 0.1801692
## 153 153 9.701752 0.1968328 7.283116 0.4740070 0.01317276 0.1804074
## 154 154 9.702899 0.1966583 7.284324 0.4733495 0.01291630 0.1793375
## 155 155 9.703793 0.1965502 7.283976 0.4741710 0.01301890 0.1812781
## 156 156 9.703775 0.1965460 7.285096 0.4747774 0.01302316 0.1822584
## 157 157 9.703450 0.1965923 7.285173 0.4748563 0.01290292 0.1819265
## 158 158 9.704328 0.1964937 7.286487 0.4765217 0.01291713 0.1843893
## 159 159 9.703783 0.1965649 7.286298 0.4770380 0.01280225 0.1851357
## 160 160 9.704398 0.1964542 7.287424 0.4760957 0.01265505 0.1841008
## 161 161 9.706109 0.1962057 7.288332 0.4752314 0.01254779 0.1821907
## 162 162 9.705268 0.1963548 7.288612 0.4759430 0.01260309 0.1825988
## 163 163 9.704030 0.1965368 7.287755 0.4763301 0.01290908 0.1833317
## 164 164 9.704904 0.1963883 7.287910 0.4763954 0.01299455 0.1832794
## 165 165 9.704869 0.1964117 7.288087 0.4755544 0.01299757 0.1821376
## 166 166 9.705688 0.1962994 7.289155 0.4741269 0.01281288 0.1807262
## 167 167 9.706337 0.1962036 7.289309 0.4741046 0.01282971 0.1811031
## 168 168 9.707204 0.1960788 7.290026 0.4730819 0.01273528 0.1797107
## 169 169 9.706935 0.1961201 7.289650 0.4732593 0.01277624 0.1793110
## 170 170 9.708322 0.1959470 7.290944 0.4732781 0.01294239 0.1796435
## 171 171 9.708910 0.1958678 7.291502 0.4738102 0.01300867 0.1804346
## 172 172 9.708427 0.1959376 7.291686 0.4727434 0.01287661 0.1793377
## 173 173 9.708569 0.1959221 7.291863 0.4719962 0.01271900 0.1788254
## 174 174 9.708397 0.1959588 7.292908 0.4726606 0.01264450 0.1804165
## 175 175 9.709438 0.1958127 7.294103 0.4715689 0.01265406 0.1796816
## 176 176 9.709590 0.1957976 7.293703 0.4714751 0.01261296 0.1798166
## 177 177 9.709657 0.1957916 7.293624 0.4711835 0.01253645 0.1792484
## 178 178 9.709536 0.1958346 7.293937 0.4721767 0.01251396 0.1799807
## 179 179 9.709915 0.1957833 7.294399 0.4719072 0.01234469 0.1799463
## 180 180 9.709841 0.1957975 7.294793 0.4729591 0.01247928 0.1806108
## 181 181 9.711130 0.1956171 7.295859 0.4728488 0.01249754 0.1808961
## 182 182 9.711023 0.1956262 7.294984 0.4726369 0.01241838 0.1802296
## 183 183 9.711936 0.1954942 7.295778 0.4715881 0.01228976 0.1787359
## 184 184 9.711634 0.1955393 7.294931 0.4712136 0.01223704 0.1784038
## 185 185 9.711150 0.1956215 7.294378 0.4715668 0.01231755 0.1780308
## 186 186 9.711510 0.1955579 7.294923 0.4707938 0.01235016 0.1779897
## 187 187 9.711915 0.1954933 7.295757 0.4702462 0.01239363 0.1769186
## 188 188 9.711401 0.1955625 7.295951 0.4688170 0.01227004 0.1763871
## 189 189 9.710433 0.1956891 7.295189 0.4687537 0.01225170 0.1772955
## 190 190 9.710355 0.1956976 7.295660 0.4679022 0.01222636 0.1763439
## 191 191 9.710399 0.1956847 7.295994 0.4675537 0.01221692 0.1766712
## 192 192 9.710990 0.1955954 7.296361 0.4679568 0.01223436 0.1773079
## 193 193 9.710467 0.1956765 7.295535 0.4681224 0.01227607 0.1769849
## 194 194 9.710846 0.1956195 7.296352 0.4672094 0.01214289 0.1765839
## 195 195 9.710998 0.1955911 7.296785 0.4679055 0.01217535 0.1769962
## 196 196 9.711544 0.1955069 7.297111 0.4674341 0.01209792 0.1768215
## 197 197 9.711157 0.1955632 7.297203 0.4679034 0.01213014 0.1774002
## 198 198 9.711459 0.1955178 7.297382 0.4676873 0.01212118 0.1780176
## 199 199 9.711763 0.1954646 7.297599 0.4679643 0.01212524 0.1783861
## 200 200 9.712089 0.1954114 7.297899 0.4680368 0.01209371 0.1783917
## 201 201 9.712238 0.1953807 7.298128 0.4677261 0.01196483 0.1782515
## 202 202 9.711818 0.1954365 7.297972 0.4677041 0.01190928 0.1783670
## 203 203 9.712314 0.1953670 7.298174 0.4673987 0.01188081 0.1785224
## 204 204 9.712486 0.1953394 7.298365 0.4675337 0.01185637 0.1785650
## 205 205 9.712728 0.1953120 7.297903 0.4672802 0.01184190 0.1783839
## 206 206 9.712803 0.1953018 7.297587 0.4676906 0.01185774 0.1786131
## 207 207 9.712969 0.1952781 7.297248 0.4676472 0.01190249 0.1789977
## 208 208 9.712667 0.1953237 7.296395 0.4675527 0.01188236 0.1789837
## 209 209 9.712865 0.1952924 7.296892 0.4674923 0.01190615 0.1790308
## 210 210 9.713115 0.1952646 7.297339 0.4672453 0.01197762 0.1788344
## 211 211 9.713154 0.1952639 7.297791 0.4681307 0.01201334 0.1790310
## 212 212 9.713887 0.1951644 7.298022 0.4675123 0.01197150 0.1789742
## 213 213 9.714192 0.1951190 7.298356 0.4672243 0.01199485 0.1787955
## 214 214 9.713905 0.1951595 7.298138 0.4673039 0.01203417 0.1786011
## 215 215 9.714339 0.1950940 7.298358 0.4674120 0.01202189 0.1787510
## 216 216 9.714256 0.1951055 7.298302 0.4678542 0.01204842 0.1789006
## 217 217 9.714555 0.1950657 7.298322 0.4680558 0.01208133 0.1793217
## 218 218 9.714872 0.1950193 7.298600 0.4680072 0.01207305 0.1790553
## 219 219 9.715020 0.1949969 7.298801 0.4680128 0.01202056 0.1790669
## 220 220 9.715131 0.1949851 7.298787 0.4680137 0.01203149 0.1789404
## 221 221 9.714983 0.1950076 7.298457 0.4680670 0.01203679 0.1790190
## 222 222 9.715141 0.1949809 7.298526 0.4681280 0.01203892 0.1789291
## 223 223 9.715082 0.1949882 7.298287 0.4682542 0.01201889 0.1791110
## 224 224 9.714937 0.1950070 7.298181 0.4682870 0.01203512 0.1789567
## 225 225 9.714871 0.1950169 7.298085 0.4683098 0.01205612 0.1789740
## 226 226 9.714810 0.1950258 7.298019 0.4683111 0.01207395 0.1789807
## 227 227 9.714748 0.1950348 7.297978 0.4683425 0.01206339 0.1788580
## 228 228 9.714570 0.1950627 7.297876 0.4682231 0.01203648 0.1788234
## 229 229 9.714722 0.1950428 7.297807 0.4681169 0.01203121 0.1787872
## 230 230 9.714694 0.1950496 7.297892 0.4682335 0.01205692 0.1788896
## 231 231 9.714536 0.1950721 7.297934 0.4683308 0.01207297 0.1788853
## 232 232 9.714408 0.1950926 7.297743 0.4683593 0.01207440 0.1787876
## 233 233 9.714291 0.1951097 7.297615 0.4683927 0.01207864 0.1787479
## 234 234 9.714310 0.1951048 7.297683 0.4683408 0.01206610 0.1786733
## 235 235 9.714420 0.1950895 7.297781 0.4682275 0.01204521 0.1785377
## 236 236 9.714438 0.1950871 7.297812 0.4682926 0.01205669 0.1786077
## 237 237 9.714535 0.1950727 7.297864 0.4683203 0.01206595 0.1786126
## 238 238 9.714524 0.1950741 7.297823 0.4682732 0.01206230 0.1785109
## 239 239 9.714518 0.1950747 7.297805 0.4682435 0.01206008 0.1784736
## 240 240 9.714503 0.1950768 7.297804 0.4682653 0.01206096 0.1784811
## nvmax
## 16 16## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'## Coefficients of final model:
## (Intercept) x4 x7 x8 x9
## 8.915934e+01 -1.285514e-02 3.239585e+00 1.274240e-01 9.675302e-01
## x10 x11 x14 x16 x17
## 3.156069e-01 5.572301e+07 -2.476429e-01 2.785612e-01 4.455166e-01
## x21 stat14 stat60 stat98 stat110
## 3.868375e-02 -2.780175e-01 1.943018e-01 9.511989e-01 -9.339451e-01
## stat149 sqrt.x18
## -2.077902e-01 7.634949e+00Test
if (algo.forward.caret == TRUE){
test.model(model.forward, data.test
,method = 'leapForward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 109.5 121.8 125.5 125.3 128.9 139.2
## [1] "leapForward Test MSE: 89.7272576325162"
Forward Selection with CV (w/ filtered train)
Train
if (algo.forward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train2
,method = "leapForward"
,feature.names = feature.names)
model.forward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 25 on full training set
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 8.270268 0.1500471 6.662698 0.1634449 0.02514052 0.11664558
## 2 2 7.968058 0.2109679 6.442396 0.1268344 0.02841881 0.10963931
## 3 3 7.845842 0.2351572 6.312228 0.1026749 0.02303243 0.08405260
## 4 4 7.665810 0.2697308 6.108489 0.1030712 0.02687427 0.08085558
## 5 5 7.567646 0.2882837 6.030670 0.1017884 0.02394369 0.06889467
## 6 6 7.533046 0.2946383 6.009967 0.1156649 0.02350019 0.07647690
## 7 7 7.535902 0.2941827 6.019534 0.1327010 0.02479979 0.08794715
## 8 8 7.508355 0.2992123 6.004663 0.1307841 0.02582231 0.07862328
## 9 9 7.494092 0.3018055 5.993913 0.1243981 0.02715968 0.06523736
## 10 10 7.462905 0.3076898 5.979216 0.1372392 0.02736091 0.07700172
## 11 11 7.458523 0.3084401 5.980278 0.1231068 0.02589088 0.07232327
## 12 12 7.449626 0.3101415 5.974128 0.1254919 0.02653904 0.07458857
## 13 13 7.454874 0.3092337 5.979360 0.1242300 0.02825630 0.07645168
## 14 14 7.453214 0.3095297 5.976030 0.1223252 0.02822013 0.07732297
## 15 15 7.449280 0.3102724 5.971021 0.1151265 0.02790063 0.07012068
## 16 16 7.444276 0.3112004 5.970120 0.1154449 0.02691800 0.07071957
## 17 17 7.440095 0.3119942 5.967821 0.1169938 0.02652318 0.06798628
## 18 18 7.440130 0.3120168 5.965993 0.1183647 0.02690668 0.06101065
## 19 19 7.441290 0.3117618 5.967720 0.1168226 0.02674273 0.06442633
## 20 20 7.441318 0.3117632 5.965754 0.1133204 0.02650599 0.06939826
## 21 21 7.440622 0.3118520 5.966512 0.1103750 0.02631120 0.06815638
## 22 22 7.440998 0.3117458 5.969405 0.1191910 0.02662217 0.07874878
## 23 23 7.435117 0.3128166 5.966475 0.1207472 0.02666011 0.08155604
## 24 24 7.432376 0.3133242 5.965317 0.1254714 0.02589745 0.08350975
## 25 25 7.427174 0.3142952 5.964074 0.1294530 0.02629751 0.08569100
## 26 26 7.429442 0.3139101 5.966334 0.1344782 0.02593492 0.08786604
## 27 27 7.427748 0.3142256 5.965396 0.1313313 0.02542731 0.09020651
## 28 28 7.429214 0.3139957 5.962745 0.1334063 0.02596286 0.09184781
## 29 29 7.430217 0.3138036 5.961525 0.1325573 0.02536088 0.09063551
## 30 30 7.440097 0.3121188 5.968205 0.1298426 0.02542237 0.08890297
## 31 31 7.444771 0.3112715 5.977173 0.1272735 0.02532592 0.09180902
## 32 32 7.444878 0.3112641 5.979971 0.1224227 0.02455986 0.09012671
## 33 33 7.445885 0.3110726 5.979526 0.1236085 0.02401712 0.08980373
## 34 34 7.445626 0.3111787 5.978867 0.1253440 0.02489009 0.09395457
## 35 35 7.441395 0.3119534 5.974747 0.1252453 0.02560298 0.09260965
## 36 36 7.440648 0.3120748 5.973807 0.1193399 0.02529007 0.08732982
## 37 37 7.442962 0.3116909 5.975630 0.1216648 0.02562119 0.09095096
## 38 38 7.442412 0.3117821 5.973954 0.1218490 0.02602849 0.09121098
## 39 39 7.442598 0.3117782 5.972167 0.1256833 0.02614503 0.09300098
## 40 40 7.442805 0.3117393 5.970514 0.1228850 0.02563324 0.09046133
## 41 41 7.445802 0.3112128 5.973407 0.1233882 0.02567731 0.08913011
## 42 42 7.449408 0.3105592 5.972936 0.1236915 0.02507956 0.09143774
## 43 43 7.449528 0.3106066 5.971538 0.1230836 0.02516070 0.08765994
## 44 44 7.453206 0.3099597 5.974107 0.1218569 0.02510287 0.08575292
## 45 45 7.453484 0.3099543 5.974780 0.1175544 0.02480624 0.08334188
## 46 46 7.455944 0.3095406 5.976069 0.1152637 0.02464170 0.08321687
## 47 47 7.459377 0.3089597 5.979902 0.1173873 0.02453286 0.08594782
## 48 48 7.461796 0.3085288 5.982447 0.1184955 0.02457746 0.08663813
## 49 49 7.463048 0.3083639 5.985049 0.1181291 0.02438431 0.08742086
## 50 50 7.459353 0.3090088 5.982509 0.1138181 0.02428897 0.08488453
## 51 51 7.462043 0.3085774 5.985365 0.1140168 0.02355532 0.08634531
## 52 52 7.467122 0.3076748 5.990979 0.1157259 0.02325294 0.08632610
## 53 53 7.465251 0.3080268 5.990840 0.1131516 0.02296230 0.08356098
## 54 54 7.465957 0.3079242 5.991513 0.1128910 0.02287662 0.08050085
## 55 55 7.468312 0.3075051 5.995625 0.1099708 0.02284868 0.08148916
## 56 56 7.466986 0.3078223 5.994806 0.1086112 0.02325644 0.07999971
## 57 57 7.469957 0.3073400 5.997396 0.1092637 0.02306459 0.08070797
## 58 58 7.471621 0.3070810 5.999736 0.1074300 0.02222463 0.07838039
## 59 59 7.470825 0.3072585 5.999289 0.1057350 0.02193570 0.07622383
## 60 60 7.473588 0.3068190 6.002796 0.1069777 0.02209823 0.07536617
## 61 61 7.476660 0.3063028 6.005636 0.1082740 0.02216860 0.07834810
## 62 62 7.478868 0.3060146 6.008861 0.1077693 0.02261928 0.07708483
## 63 63 7.479903 0.3058375 6.010008 0.1109536 0.02312981 0.07853411
## 64 64 7.478866 0.3060280 6.008061 0.1119872 0.02284084 0.07982082
## 65 65 7.478129 0.3061734 6.007900 0.1126481 0.02285274 0.07715136
## 66 66 7.479692 0.3059370 6.008461 0.1116280 0.02254632 0.07681134
## 67 67 7.480111 0.3058822 6.009286 0.1109875 0.02266821 0.07567262
## 68 68 7.482207 0.3055123 6.008609 0.1091504 0.02240214 0.07714594
## 69 69 7.486912 0.3046667 6.011446 0.1099665 0.02254978 0.07885999
## 70 70 7.488661 0.3043204 6.013690 0.1101729 0.02300409 0.07762739
## 71 71 7.490095 0.3040953 6.012778 0.1069016 0.02253847 0.07718172
## 72 72 7.487522 0.3045653 6.010362 0.1085314 0.02258771 0.07692798
## 73 73 7.491067 0.3039543 6.011479 0.1102704 0.02257665 0.07627820
## 74 74 7.489593 0.3042320 6.008483 0.1105368 0.02239445 0.07760376
## 75 75 7.489335 0.3042884 6.007267 0.1089574 0.02176076 0.07771407
## 76 76 7.489192 0.3043032 6.007889 0.1080697 0.02175223 0.07743033
## 77 77 7.492471 0.3037168 6.011622 0.1109915 0.02218919 0.07784873
## 78 78 7.491123 0.3039630 6.009826 0.1108366 0.02182508 0.07696699
## 79 79 7.493623 0.3035433 6.012968 0.1133333 0.02191099 0.07965836
## 80 80 7.496128 0.3031225 6.016288 0.1151013 0.02207166 0.08176575
## 81 81 7.497192 0.3029380 6.016782 0.1166381 0.02242902 0.08091844
## 82 82 7.498704 0.3026781 6.018075 0.1172161 0.02259895 0.08069463
## 83 83 7.497677 0.3028554 6.016341 0.1161906 0.02241198 0.07935873
## 84 84 7.498873 0.3026410 6.017504 0.1139553 0.02267429 0.07627491
## 85 85 7.499630 0.3024967 6.018971 0.1133166 0.02221965 0.07589524
## 86 86 7.499632 0.3025001 6.019992 0.1126004 0.02193522 0.07558983
## 87 87 7.498399 0.3027628 6.018779 0.1136247 0.02231431 0.07415636
## 88 88 7.498050 0.3028383 6.018258 0.1138690 0.02286849 0.07634811
## 89 89 7.500039 0.3025096 6.020762 0.1121790 0.02257205 0.07466242
## 90 90 7.500577 0.3024012 6.020266 0.1117078 0.02290882 0.07364084
## 91 91 7.503348 0.3019564 6.022355 0.1108911 0.02308335 0.07379244
## 92 92 7.505298 0.3016400 6.024415 0.1125407 0.02312746 0.07310374
## 93 93 7.506069 0.3015029 6.025474 0.1123178 0.02327143 0.07337420
## 94 94 7.506691 0.3013748 6.026434 0.1112739 0.02325794 0.07181309
## 95 95 7.508718 0.3010343 6.027137 0.1138424 0.02367179 0.07293358
## 96 96 7.508815 0.3010371 6.027991 0.1131569 0.02332011 0.07413567
## 97 97 7.507330 0.3012789 6.025938 0.1134037 0.02350063 0.07533998
## 98 98 7.507389 0.3013046 6.025220 0.1154150 0.02381778 0.07658415
## 99 99 7.507372 0.3013426 6.024486 0.1149714 0.02386084 0.07637061
## 100 100 7.510772 0.3007759 6.026165 0.1156640 0.02419904 0.07460874
## 101 101 7.513989 0.3002482 6.029011 0.1141307 0.02377557 0.07142174
## 102 102 7.514069 0.3002620 6.029178 0.1136962 0.02382378 0.07041645
## 103 103 7.513946 0.3003022 6.029506 0.1120439 0.02342939 0.07034174
## 104 104 7.512351 0.3005781 6.029149 0.1115112 0.02293943 0.06831959
## 105 105 7.511595 0.3007127 6.029099 0.1118315 0.02332256 0.06850534
## 106 106 7.510564 0.3008803 6.028673 0.1099502 0.02313356 0.06833307
## 107 107 7.511653 0.3006873 6.030064 0.1110148 0.02316931 0.06987855
## 108 108 7.512708 0.3005078 6.032113 0.1112512 0.02296502 0.07040914
## 109 109 7.512616 0.3005389 6.032861 0.1112510 0.02291141 0.07102883
## 110 110 7.511458 0.3007619 6.031451 0.1114071 0.02272162 0.07095806
## 111 111 7.512373 0.3006261 6.030977 0.1115426 0.02304710 0.06995038
## 112 112 7.513550 0.3004189 6.032129 0.1091202 0.02266398 0.06817279
## 113 113 7.512971 0.3005303 6.030360 0.1066508 0.02237106 0.06614822
## 114 114 7.514045 0.3003552 6.030793 0.1038330 0.02203353 0.06486954
## 115 115 7.514966 0.3002040 6.030393 0.1074759 0.02265177 0.06609847
## 116 116 7.513226 0.3005122 6.029271 0.1057840 0.02236629 0.06501921
## 117 117 7.513954 0.3003961 6.029629 0.1070904 0.02237677 0.06566215
## 118 118 7.514228 0.3003537 6.029062 0.1048589 0.02228375 0.06501220
## 119 119 7.514534 0.3003191 6.028660 0.1052240 0.02218524 0.06542715
## 120 120 7.514119 0.3004105 6.028813 0.1040377 0.02199159 0.06340077
## 121 121 7.513177 0.3005822 6.027766 0.1030436 0.02171990 0.06352734
## 122 122 7.514933 0.3002861 6.029130 0.1023427 0.02149532 0.06199668
## 123 123 7.514612 0.3003394 6.027733 0.1015061 0.02175213 0.06053374
## 124 124 7.515326 0.3002263 6.027241 0.1019193 0.02160247 0.06175342
## 125 125 7.514628 0.3003542 6.027844 0.1010022 0.02165998 0.06105032
## 126 126 7.513457 0.3005475 6.028666 0.1018181 0.02164524 0.06053405
## 127 127 7.513630 0.3005379 6.028438 0.1019516 0.02164159 0.06010594
## 128 128 7.513752 0.3005187 6.028276 0.1021789 0.02153731 0.06028771
## 129 129 7.515089 0.3003006 6.029891 0.1018954 0.02141692 0.06019921
## 130 130 7.514689 0.3003809 6.028983 0.1013580 0.02156691 0.05917609
## 131 131 7.514708 0.3003753 6.028429 0.1013665 0.02135761 0.05909878
## 132 132 7.516083 0.3001637 6.029147 0.1016555 0.02165498 0.05868222
## 133 133 7.516431 0.3001149 6.028960 0.1011161 0.02149746 0.05780008
## 134 134 7.517690 0.2999097 6.029814 0.1018319 0.02135776 0.05989409
## 135 135 7.517702 0.2999289 6.029074 0.1017248 0.02111938 0.06051169
## 136 136 7.518157 0.2998427 6.030305 0.1014238 0.02102514 0.06108282
## 137 137 7.517757 0.2999297 6.030181 0.1019799 0.02094653 0.06228239
## 138 138 7.517045 0.3000390 6.029667 0.1027932 0.02081884 0.06189751
## 139 139 7.516063 0.3002359 6.028344 0.1026755 0.02070114 0.06199464
## 140 140 7.517522 0.2999763 6.029956 0.1024743 0.02064481 0.06194764
## 141 141 7.519483 0.2996390 6.030881 0.1026182 0.02052642 0.06343300
## 142 142 7.519294 0.2996890 6.031170 0.1021568 0.02065282 0.06277534
## 143 143 7.518823 0.2997632 6.031473 0.1025441 0.02065702 0.06352936
## 144 144 7.519565 0.2996449 6.032798 0.1030805 0.02081231 0.06364566
## 145 145 7.519627 0.2996240 6.031746 0.1015581 0.02066747 0.06296099
## 146 146 7.519517 0.2996472 6.031152 0.1023821 0.02060756 0.06444646
## 147 147 7.518858 0.2997573 6.030186 0.1035761 0.02076447 0.06414505
## 148 148 7.519107 0.2997208 6.030530 0.1038064 0.02060571 0.06468727
## 149 149 7.520547 0.2994740 6.032297 0.1043311 0.02040829 0.06564955
## 150 150 7.518600 0.2998079 6.030471 0.1035622 0.02033565 0.06439091
## 151 151 7.520402 0.2994956 6.031925 0.1040387 0.02045204 0.06483379
## 152 152 7.520202 0.2995470 6.031333 0.1040515 0.02028831 0.06489592
## 153 153 7.520610 0.2995007 6.032067 0.1051110 0.02033285 0.06607826
## 154 154 7.521053 0.2994436 6.032060 0.1065442 0.02032910 0.06692107
## 155 155 7.521313 0.2993986 6.032413 0.1065159 0.02032982 0.06638972
## 156 156 7.521723 0.2993222 6.032689 0.1073371 0.02036017 0.06648148
## 157 157 7.523000 0.2991221 6.033497 0.1079159 0.02049118 0.06626059
## 158 158 7.523528 0.2990500 6.033301 0.1087719 0.02080115 0.06672511
## 159 159 7.523403 0.2990639 6.033945 0.1093470 0.02085636 0.06675413
## 160 160 7.523595 0.2990113 6.033420 0.1081599 0.02066453 0.06661192
## 161 161 7.522453 0.2992062 6.032641 0.1083264 0.02064215 0.06644176
## 162 162 7.521227 0.2994014 6.031580 0.1073415 0.02043135 0.06566283
## 163 163 7.521202 0.2994222 6.031710 0.1073914 0.02023327 0.06620060
## 164 164 7.520897 0.2994872 6.031651 0.1080092 0.02031412 0.06694421
## 165 165 7.519642 0.2997038 6.030683 0.1075389 0.02036778 0.06714883
## 166 166 7.518879 0.2998429 6.030515 0.1077509 0.02041933 0.06721970
## 167 167 7.519845 0.2996643 6.031492 0.1075427 0.02061256 0.06725612
## 168 168 7.519020 0.2998088 6.030716 0.1073489 0.02052365 0.06704497
## 169 169 7.518536 0.2998975 6.030977 0.1073848 0.02052666 0.06691760
## 170 170 7.519101 0.2997918 6.031995 0.1073436 0.02046539 0.06714953
## 171 171 7.519949 0.2996521 6.033029 0.1067274 0.02031049 0.06658036
## 172 172 7.519211 0.2997681 6.032805 0.1067635 0.02043361 0.06591621
## 173 173 7.518766 0.2998333 6.032578 0.1067360 0.02043129 0.06623556
## 174 174 7.518527 0.2998760 6.032518 0.1060126 0.02040578 0.06588960
## 175 175 7.518359 0.2999037 6.032467 0.1065693 0.02033673 0.06580136
## 176 176 7.518244 0.2999244 6.032537 0.1066673 0.02017576 0.06675605
## 177 177 7.518063 0.2999531 6.033107 0.1062654 0.02003956 0.06698244
## 178 178 7.517901 0.2999910 6.033461 0.1066969 0.02000254 0.06719302
## 179 179 7.516961 0.3001535 6.032418 0.1068486 0.02002172 0.06776576
## 180 180 7.517721 0.3000275 6.033410 0.1064531 0.01994890 0.06725342
## 181 181 7.517129 0.3001251 6.032988 0.1067106 0.01999003 0.06696726
## 182 182 7.517032 0.3001428 6.033213 0.1065569 0.01994929 0.06747090
## 183 183 7.516996 0.3001490 6.033505 0.1055645 0.01995687 0.06607726
## 184 184 7.516829 0.3001780 6.033253 0.1059749 0.01993253 0.06670456
## 185 185 7.516247 0.3002906 6.033561 0.1061081 0.01997384 0.06692649
## 186 186 7.515972 0.3003390 6.033279 0.1053207 0.02003371 0.06564276
## 187 187 7.516490 0.3002548 6.033733 0.1057648 0.01986562 0.06603702
## 188 188 7.516941 0.3001723 6.034350 0.1051718 0.01968720 0.06569393
## 189 189 7.516200 0.3003076 6.033551 0.1046592 0.01969228 0.06527864
## 190 190 7.515749 0.3003716 6.033592 0.1045888 0.01983579 0.06505447
## 191 191 7.515807 0.3003524 6.033265 0.1037707 0.01966872 0.06481934
## 192 192 7.516476 0.3002445 6.033829 0.1033629 0.01960414 0.06423199
## 193 193 7.516655 0.3002192 6.034383 0.1035111 0.01968692 0.06377296
## 194 194 7.516327 0.3002808 6.033780 0.1041488 0.01972615 0.06401268
## 195 195 7.516151 0.3003140 6.033395 0.1044211 0.01967452 0.06464955
## 196 196 7.515816 0.3003699 6.032761 0.1047470 0.01984963 0.06440233
## 197 197 7.515835 0.3003686 6.032666 0.1041556 0.01973065 0.06366082
## 198 198 7.516298 0.3002913 6.033040 0.1044994 0.01976181 0.06408948
## 199 199 7.515695 0.3003899 6.032339 0.1044972 0.01973181 0.06394727
## 200 200 7.516052 0.3003316 6.032764 0.1045228 0.01978865 0.06314028
## 201 201 7.516434 0.3002569 6.033279 0.1041104 0.01974387 0.06336424
## 202 202 7.516036 0.3003287 6.032685 0.1037726 0.01982285 0.06308160
## 203 203 7.515731 0.3003807 6.032575 0.1040710 0.01975302 0.06362317
## 204 204 7.515598 0.3004055 6.032077 0.1037319 0.01971876 0.06337082
## 205 205 7.515233 0.3004672 6.031563 0.1038177 0.01976092 0.06353169
## 206 206 7.515352 0.3004440 6.031727 0.1043152 0.01973340 0.06379095
## 207 207 7.515428 0.3004288 6.031680 0.1047298 0.01972795 0.06435322
## 208 208 7.515083 0.3004870 6.031357 0.1044821 0.01969237 0.06448936
## 209 209 7.515555 0.3004112 6.031945 0.1038538 0.01960536 0.06439284
## 210 210 7.515583 0.3004160 6.032081 0.1034344 0.01962462 0.06400060
## 211 211 7.514964 0.3005245 6.031261 0.1033488 0.01962963 0.06386220
## 212 212 7.514951 0.3005284 6.031379 0.1031330 0.01973268 0.06363633
## 213 213 7.514631 0.3005875 6.031082 0.1026906 0.01969156 0.06345399
## 214 214 7.514046 0.3006847 6.030390 0.1026815 0.01971050 0.06334877
## 215 215 7.514162 0.3006612 6.030339 0.1027709 0.01970342 0.06317489
## 216 216 7.514219 0.3006512 6.030363 0.1028697 0.01966107 0.06327584
## 217 217 7.513932 0.3007048 6.030002 0.1030286 0.01965270 0.06324843
## 218 218 7.513932 0.3007022 6.029944 0.1027652 0.01964202 0.06297415
## 219 219 7.513788 0.3007318 6.029779 0.1026667 0.01964564 0.06278031
## 220 220 7.513834 0.3007246 6.029968 0.1024377 0.01959591 0.06292932
## 221 221 7.514031 0.3006899 6.030045 0.1025461 0.01964483 0.06259663
## 222 222 7.514187 0.3006640 6.030012 0.1025661 0.01960866 0.06247228
## 223 223 7.513945 0.3007056 6.029742 0.1026614 0.01961009 0.06258606
## 224 224 7.513930 0.3007118 6.029786 0.1026362 0.01964959 0.06254641
## 225 225 7.513770 0.3007401 6.029577 0.1024963 0.01962453 0.06260621
## 226 226 7.513661 0.3007630 6.029545 0.1026501 0.01968100 0.06263315
## 227 227 7.513504 0.3007871 6.029471 0.1023918 0.01964694 0.06265606
## 228 228 7.513511 0.3007858 6.029552 0.1024293 0.01966040 0.06258867
## 229 229 7.513521 0.3007838 6.029502 0.1020795 0.01965917 0.06235755
## 230 230 7.513227 0.3008357 6.029330 0.1021693 0.01964450 0.06254157
## 231 231 7.513332 0.3008164 6.029465 0.1021261 0.01962689 0.06255784
## 232 232 7.513532 0.3007804 6.029636 0.1020927 0.01962129 0.06254178
## 233 233 7.513489 0.3007880 6.029626 0.1020469 0.01962357 0.06249576
## 234 234 7.513532 0.3007808 6.029729 0.1020161 0.01962047 0.06254948
## 235 235 7.513564 0.3007764 6.029752 0.1019786 0.01963529 0.06253389
## 236 236 7.513592 0.3007697 6.029811 0.1019815 0.01962200 0.06254947
## 237 237 7.513596 0.3007691 6.029771 0.1019959 0.01961401 0.06255203
## 238 238 7.513563 0.3007753 6.029785 0.1018913 0.01961497 0.06243028
## 239 239 7.513563 0.3007754 6.029787 0.1019127 0.01962115 0.06241481
## 240 240 7.513584 0.3007718 6.029796 0.1019202 0.01962246 0.06241429
## nvmax
## 25 25## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'## Coefficients of final model:
## (Intercept) x4 x7 x8 x9
## 8.733025e+01 -1.487732e-02 3.352477e+00 1.410604e-01 9.451043e-01
## x10 x11 x16 x17 x21
## 4.253677e-01 5.771201e+07 2.555669e-01 4.181964e-01 3.566003e-02
## stat4 stat13 stat14 stat23 stat25
## -1.636272e-01 -1.831055e-01 -3.085334e-01 1.948212e-01 -1.437340e-01
## stat38 stat41 stat60 stat85 stat98
## 1.589337e-01 -1.702179e-01 1.948465e-01 -1.431581e-01 8.584054e-01
## stat110 stat128 stat144 stat146 stat149
## -8.961450e-01 -1.604357e-01 1.596797e-01 -1.498132e-01 -2.043875e-01
## sqrt.x18
## 7.454872e+00Test
if (algo.forward.caret == TRUE){
test.model(model.forward, data.test
,method = 'leapForward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 107.3 120.7 124.3 124.1 127.8 138.1
## [1] "leapForward Test MSE: 91.2164226586688"
Backward Elimination
Train
if (algo.backward == TRUE){
# Takes too much time
t1 = Sys.time()
model.backward = step(model.full, data = data.train, direction="backward", trace = 0)
print(summary(model.backward))
#saveRDS(model.forward,file = "model_backward.rds")
t2 = Sys.time()
print (paste("Time taken for Backward Elimination: ",t2-t1, sep = ""))
plot.diagnostics(model.backward, data.train)
}Test
if (algo.backward == TRUE){
test.model(model.backard, data.test, "Backward Elimination")
}Backward Elimination with CV (w/ full train)
Train
if (algo.backward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapBackward"
,feature.names = feature.names)
model.backward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 19 on full training set
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 10.205848 0.1070230 7.793298 0.4837937 0.02121144 0.2343155
## 2 2 9.978578 0.1456242 7.594919 0.4865059 0.01542500 0.2210630
## 3 3 9.869319 0.1645156 7.472217 0.4757917 0.01700325 0.2032220
## 4 4 9.705345 0.1918124 7.255723 0.4773872 0.01219753 0.1920870
## 5 5 9.623121 0.2056678 7.191041 0.5001426 0.01530975 0.2093101
## 6 6 9.615614 0.2067906 7.190418 0.4962592 0.01340840 0.1969631
## 7 7 9.599094 0.2094876 7.178668 0.4953228 0.01391436 0.2006617
## 8 8 9.581185 0.2124654 7.171670 0.4983385 0.01423833 0.2054035
## 9 9 9.573978 0.2136032 7.160477 0.4946051 0.01182847 0.1967355
## 10 10 9.566457 0.2148079 7.156153 0.4890367 0.01057451 0.1936818
## 11 11 9.569889 0.2143339 7.162311 0.4933912 0.01197829 0.2041986
## 12 12 9.572535 0.2139549 7.164093 0.4913304 0.01123655 0.2012837
## 13 13 9.571512 0.2141605 7.161750 0.4913776 0.01141375 0.1948090
## 14 14 9.569202 0.2145821 7.160108 0.4886390 0.01088688 0.1991866
## 15 15 9.568774 0.2146047 7.157827 0.4818420 0.01068948 0.1909961
## 16 16 9.565261 0.2152305 7.160380 0.4895184 0.01216199 0.1976081
## 17 17 9.567334 0.2149625 7.164737 0.4913768 0.01360563 0.2009011
## 18 18 9.567337 0.2149964 7.164855 0.4874672 0.01361163 0.1994390
## 19 19 9.562362 0.2158963 7.158834 0.4926740 0.01415188 0.2033848
## 20 20 9.571302 0.2145096 7.165829 0.4932075 0.01386646 0.2024829
## 21 21 9.567416 0.2152074 7.159803 0.4941473 0.01404452 0.2018575
## 22 22 9.571406 0.2145969 7.160732 0.4957266 0.01458413 0.2060193
## 23 23 9.575463 0.2139494 7.163199 0.4969331 0.01432135 0.2027895
## 24 24 9.583368 0.2127542 7.167614 0.4983340 0.01469583 0.2017528
## 25 25 9.582286 0.2129563 7.167646 0.4950203 0.01322326 0.2028330
## 26 26 9.590248 0.2117843 7.176497 0.4999595 0.01418107 0.2090227
## 27 27 9.595746 0.2109382 7.182070 0.4973136 0.01393394 0.2086277
## 28 28 9.598859 0.2104611 7.186796 0.4985010 0.01415490 0.2086077
## 29 29 9.594474 0.2111133 7.184776 0.4965284 0.01417496 0.2039828
## 30 30 9.596270 0.2108588 7.183074 0.4922937 0.01378263 0.2003609
## 31 31 9.596107 0.2109165 7.181586 0.4940167 0.01456892 0.1995700
## 32 32 9.599148 0.2104233 7.183031 0.4919426 0.01432897 0.1950352
## 33 33 9.605265 0.2094508 7.187569 0.4850093 0.01363172 0.1890039
## 34 34 9.611314 0.2085646 7.194728 0.4857052 0.01354462 0.1924132
## 35 35 9.617041 0.2077382 7.198578 0.4857869 0.01397109 0.1914110
## 36 36 9.615917 0.2079240 7.196450 0.4812063 0.01334848 0.1876855
## 37 37 9.619457 0.2073523 7.199992 0.4796731 0.01333185 0.1840511
## 38 38 9.624640 0.2065558 7.203557 0.4839502 0.01363285 0.1884245
## 39 39 9.625910 0.2063444 7.205746 0.4843659 0.01366364 0.1855229
## 40 40 9.627995 0.2060514 7.205733 0.4880815 0.01350262 0.1872512
## 41 41 9.629037 0.2059215 7.208334 0.4927490 0.01329750 0.1911551
## 42 42 9.630054 0.2057674 7.209988 0.4917740 0.01310605 0.1928935
## 43 43 9.628893 0.2059596 7.208163 0.4967871 0.01409955 0.1995894
## 44 44 9.630327 0.2057774 7.211031 0.4962014 0.01416086 0.1998333
## 45 45 9.626998 0.2063329 7.207696 0.4929560 0.01347146 0.1956042
## 46 46 9.628639 0.2061246 7.209790 0.4914027 0.01335489 0.1952665
## 47 47 9.628160 0.2062468 7.210923 0.4949744 0.01365686 0.1945632
## 48 48 9.632717 0.2055818 7.216487 0.4980589 0.01385014 0.1971969
## 49 49 9.635753 0.2051288 7.220327 0.4947335 0.01368369 0.1973255
## 50 50 9.639846 0.2044955 7.226929 0.4915806 0.01320375 0.1943038
## 51 51 9.640975 0.2043166 7.228632 0.4902914 0.01260944 0.1915218
## 52 52 9.640461 0.2044317 7.226599 0.4892529 0.01221077 0.1931629
## 53 53 9.647393 0.2034604 7.232237 0.4895990 0.01177643 0.1951494
## 54 54 9.648265 0.2033883 7.235465 0.4905796 0.01197122 0.1973725
## 55 55 9.652948 0.2027337 7.239494 0.4909526 0.01209016 0.1958505
## 56 56 9.650763 0.2031109 7.236628 0.4898040 0.01190569 0.1979289
## 57 57 9.650222 0.2031639 7.235884 0.4903489 0.01206302 0.1978371
## 58 58 9.651924 0.2029351 7.237053 0.4905861 0.01223864 0.1967341
## 59 59 9.655341 0.2024556 7.241885 0.4901514 0.01253511 0.1947968
## 60 60 9.655501 0.2024204 7.240196 0.4862630 0.01212228 0.1924294
## 61 61 9.654554 0.2026047 7.240115 0.4882100 0.01228887 0.1943175
## 62 62 9.657116 0.2022238 7.241827 0.4848064 0.01230450 0.1929553
## 63 63 9.657260 0.2022973 7.242278 0.4860896 0.01244360 0.1911007
## 64 64 9.661599 0.2016982 7.246358 0.4879359 0.01234891 0.1946322
## 65 65 9.662127 0.2016721 7.245871 0.4869920 0.01241064 0.1928998
## 66 66 9.659061 0.2020945 7.245111 0.4858542 0.01193031 0.1918886
## 67 67 9.662760 0.2015754 7.249590 0.4889833 0.01295215 0.1944322
## 68 68 9.663287 0.2015348 7.250182 0.4905008 0.01329477 0.1949880
## 69 69 9.663812 0.2014996 7.249044 0.4920350 0.01387285 0.1946294
## 70 70 9.664004 0.2014832 7.248936 0.4908428 0.01368468 0.1955668
## 71 71 9.665785 0.2012074 7.249414 0.4887005 0.01348347 0.1934958
## 72 72 9.662739 0.2016769 7.245371 0.4902772 0.01352472 0.1948359
## 73 73 9.659178 0.2021951 7.243435 0.4873207 0.01282282 0.1917531
## 74 74 9.659354 0.2021668 7.243297 0.4886869 0.01312672 0.1913921
## 75 75 9.662708 0.2016938 7.247164 0.4873989 0.01310814 0.1928876
## 76 76 9.660173 0.2020983 7.246713 0.4890875 0.01327009 0.1980937
## 77 77 9.657581 0.2025171 7.243160 0.4898856 0.01327790 0.1972201
## 78 78 9.655852 0.2028058 7.243931 0.4897605 0.01299943 0.1976480
## 79 79 9.656670 0.2027133 7.244318 0.4887119 0.01296953 0.1962015
## 80 80 9.656751 0.2026972 7.244483 0.4853217 0.01261353 0.1946568
## 81 81 9.657590 0.2026273 7.242976 0.4838482 0.01262482 0.1952410
## 82 82 9.658435 0.2025202 7.244680 0.4834751 0.01235412 0.1928695
## 83 83 9.662127 0.2019762 7.249442 0.4816685 0.01228831 0.1927000
## 84 84 9.661492 0.2020600 7.249307 0.4776277 0.01170593 0.1900698
## 85 85 9.662195 0.2019749 7.249292 0.4789569 0.01181229 0.1914320
## 86 86 9.664893 0.2016151 7.250713 0.4840073 0.01257959 0.1940915
## 87 87 9.663427 0.2018458 7.249138 0.4799809 0.01217629 0.1897677
## 88 88 9.662724 0.2019658 7.248019 0.4804455 0.01195451 0.1870421
## 89 89 9.662850 0.2019935 7.245907 0.4812640 0.01241939 0.1872390
## 90 90 9.663355 0.2019261 7.245993 0.4847845 0.01294216 0.1874928
## 91 91 9.665010 0.2017166 7.248325 0.4858344 0.01288464 0.1878946
## 92 92 9.664952 0.2017875 7.246514 0.4849091 0.01274396 0.1885734
## 93 93 9.666339 0.2015984 7.247282 0.4823479 0.01256206 0.1859807
## 94 94 9.664331 0.2018923 7.246431 0.4794122 0.01217075 0.1832512
## 95 95 9.665127 0.2017707 7.247941 0.4791639 0.01237723 0.1828138
## 96 96 9.668477 0.2012688 7.251497 0.4815496 0.01256527 0.1859046
## 97 97 9.666978 0.2014895 7.252613 0.4827053 0.01265188 0.1864985
## 98 98 9.667450 0.2014402 7.253908 0.4822723 0.01278868 0.1866056
## 99 99 9.668031 0.2013767 7.253829 0.4824339 0.01313630 0.1871715
## 100 100 9.668550 0.2013107 7.254471 0.4819541 0.01308857 0.1865511
## 101 101 9.671818 0.2008735 7.257933 0.4825595 0.01328047 0.1864006
## 102 102 9.672933 0.2007423 7.261619 0.4794726 0.01308231 0.1835565
## 103 103 9.675260 0.2003845 7.263414 0.4801250 0.01310245 0.1842134
## 104 104 9.678113 0.1999659 7.267006 0.4769741 0.01263651 0.1805598
## 105 105 9.678647 0.1998938 7.267360 0.4776166 0.01280516 0.1795283
## 106 106 9.679320 0.1997921 7.267498 0.4783392 0.01281347 0.1800221
## 107 107 9.679592 0.1997363 7.269018 0.4787866 0.01275670 0.1809555
## 108 108 9.683558 0.1991634 7.270950 0.4779529 0.01267542 0.1801556
## 109 109 9.683632 0.1991690 7.270669 0.4756294 0.01276463 0.1789218
## 110 110 9.684196 0.1991168 7.269010 0.4745476 0.01245626 0.1785191
## 111 111 9.682997 0.1992939 7.267730 0.4761805 0.01249970 0.1797205
## 112 112 9.685357 0.1990080 7.269319 0.4731941 0.01245727 0.1770993
## 113 113 9.684323 0.1991568 7.268978 0.4729659 0.01238861 0.1777692
## 114 114 9.686342 0.1988415 7.269871 0.4714479 0.01231594 0.1777333
## 115 115 9.683585 0.1992545 7.269452 0.4712946 0.01201555 0.1761478
## 116 116 9.683431 0.1992946 7.269243 0.4710566 0.01235242 0.1779592
## 117 117 9.685318 0.1990309 7.270412 0.4706825 0.01221092 0.1757824
## 118 118 9.688069 0.1986369 7.273363 0.4689140 0.01223037 0.1748891
## 119 119 9.689423 0.1984399 7.273737 0.4685242 0.01242421 0.1756839
## 120 120 9.689907 0.1983832 7.273334 0.4709158 0.01255156 0.1773673
## 121 121 9.689990 0.1983714 7.273247 0.4699230 0.01231377 0.1762457
## 122 122 9.691768 0.1980836 7.274326 0.4676699 0.01237105 0.1748183
## 123 123 9.693526 0.1978605 7.277054 0.4688506 0.01266815 0.1778559
## 124 124 9.695159 0.1976130 7.277978 0.4719612 0.01297496 0.1817237
## 125 125 9.695284 0.1976208 7.278316 0.4739066 0.01333068 0.1824749
## 126 126 9.696568 0.1974569 7.280158 0.4732186 0.01338717 0.1821526
## 127 127 9.695982 0.1975423 7.279177 0.4769746 0.01364433 0.1848789
## 128 128 9.695521 0.1976446 7.277701 0.4759199 0.01356594 0.1845989
## 129 129 9.696429 0.1974800 7.279761 0.4757679 0.01338235 0.1846368
## 130 130 9.698805 0.1971310 7.282020 0.4743382 0.01339969 0.1857527
## 131 131 9.699106 0.1971150 7.281626 0.4723020 0.01334117 0.1835792
## 132 132 9.698321 0.1972344 7.280920 0.4719988 0.01340341 0.1824222
## 133 133 9.696322 0.1975384 7.277455 0.4733217 0.01341779 0.1833088
## 134 134 9.696671 0.1974814 7.277331 0.4737549 0.01334922 0.1838861
## 135 135 9.695571 0.1976440 7.275539 0.4746006 0.01332339 0.1842961
## 136 136 9.693744 0.1979135 7.273962 0.4764273 0.01358403 0.1856467
## 137 137 9.694039 0.1978612 7.274334 0.4738326 0.01345097 0.1848245
## 138 138 9.695144 0.1977176 7.276151 0.4720927 0.01312571 0.1817444
## 139 139 9.694893 0.1977780 7.275813 0.4718483 0.01298098 0.1833086
## 140 140 9.696456 0.1975507 7.276073 0.4731874 0.01302806 0.1824830
## 141 141 9.697355 0.1973908 7.277989 0.4733178 0.01298154 0.1821315
## 142 142 9.696811 0.1974788 7.277902 0.4712072 0.01290822 0.1821340
## 143 143 9.696825 0.1974950 7.278978 0.4713992 0.01307407 0.1832113
## 144 144 9.695340 0.1977258 7.278064 0.4720461 0.01302724 0.1828675
## 145 145 9.696820 0.1975326 7.280327 0.4721200 0.01309267 0.1829917
## 146 146 9.697153 0.1974531 7.280674 0.4724268 0.01296248 0.1825087
## 147 147 9.697541 0.1974018 7.280183 0.4737874 0.01315245 0.1834717
## 148 148 9.698023 0.1973398 7.280737 0.4747850 0.01308363 0.1834922
## 149 149 9.699211 0.1971698 7.280399 0.4744261 0.01306115 0.1830394
## 150 150 9.699522 0.1971329 7.280516 0.4730413 0.01304062 0.1808626
## 151 151 9.700466 0.1969917 7.282134 0.4727899 0.01285515 0.1792043
## 152 152 9.701099 0.1969241 7.282114 0.4738467 0.01298404 0.1787989
## 153 153 9.702382 0.1967478 7.283867 0.4735004 0.01302301 0.1809186
## 154 154 9.702715 0.1967085 7.283595 0.4733836 0.01305025 0.1811759
## 155 155 9.703643 0.1966020 7.284516 0.4749992 0.01324381 0.1819034
## 156 156 9.704434 0.1964620 7.285862 0.4746833 0.01305472 0.1824504
## 157 157 9.703582 0.1965975 7.284882 0.4752717 0.01300646 0.1829955
## 158 158 9.704822 0.1964176 7.286453 0.4770487 0.01307778 0.1849310
## 159 159 9.704956 0.1963881 7.286847 0.4769912 0.01289360 0.1849462
## 160 160 9.704922 0.1963727 7.286666 0.4761648 0.01272078 0.1843181
## 161 161 9.706375 0.1961559 7.287400 0.4751833 0.01259623 0.1819531
## 162 162 9.704820 0.1963931 7.287269 0.4759895 0.01258746 0.1826285
## 163 163 9.705742 0.1962494 7.288158 0.4752321 0.01260972 0.1823770
## 164 164 9.706214 0.1961806 7.288503 0.4757525 0.01269116 0.1823876
## 165 165 9.706052 0.1962390 7.288525 0.4759545 0.01283614 0.1820709
## 166 166 9.706635 0.1961672 7.289471 0.4743515 0.01268739 0.1806905
## 167 167 9.706358 0.1962067 7.289008 0.4740090 0.01282082 0.1810591
## 168 168 9.706574 0.1961781 7.289704 0.4730141 0.01286048 0.1797520
## 169 169 9.706744 0.1961576 7.289323 0.4730797 0.01289013 0.1795912
## 170 170 9.707616 0.1960468 7.290655 0.4736049 0.01297671 0.1798373
## 171 171 9.708704 0.1959023 7.291018 0.4738181 0.01301194 0.1806541
## 172 172 9.708512 0.1959377 7.291878 0.4730865 0.01291264 0.1793889
## 173 173 9.708435 0.1959423 7.292168 0.4718825 0.01275255 0.1787457
## 174 174 9.708264 0.1959788 7.293230 0.4725473 0.01267767 0.1803379
## 175 175 9.709217 0.1958498 7.294008 0.4722957 0.01269188 0.1805040
## 176 176 9.709692 0.1957876 7.293682 0.4724831 0.01257195 0.1806462
## 177 177 9.709761 0.1957814 7.293598 0.4721962 0.01249503 0.1800756
## 178 178 9.710165 0.1957496 7.294146 0.4724505 0.01243371 0.1799425
## 179 179 9.710154 0.1957548 7.294527 0.4718398 0.01235600 0.1799241
## 180 180 9.709438 0.1958595 7.293791 0.4729215 0.01241823 0.1809620
## 181 181 9.710757 0.1956829 7.295140 0.4727041 0.01242298 0.1811684
## 182 182 9.710595 0.1956963 7.294920 0.4726998 0.01239907 0.1801088
## 183 183 9.711245 0.1956000 7.294942 0.4718913 0.01227424 0.1797826
## 184 184 9.710962 0.1956467 7.294572 0.4713648 0.01225133 0.1788006
## 185 185 9.710800 0.1956699 7.294267 0.4714679 0.01227641 0.1783845
## 186 186 9.710720 0.1956717 7.294404 0.4711128 0.01232655 0.1786054
## 187 187 9.711552 0.1955414 7.295327 0.4702716 0.01237305 0.1770586
## 188 188 9.711671 0.1955185 7.295777 0.4687530 0.01225462 0.1765300
## 189 189 9.710811 0.1956323 7.295167 0.4686988 0.01224806 0.1773314
## 190 190 9.710782 0.1956394 7.295854 0.4678524 0.01222420 0.1762475
## 191 191 9.710639 0.1956503 7.295885 0.4675023 0.01219775 0.1766837
## 192 192 9.710939 0.1956028 7.296444 0.4679621 0.01223144 0.1773056
## 193 193 9.710324 0.1957035 7.295521 0.4681368 0.01226489 0.1769850
## 194 194 9.710775 0.1956320 7.296402 0.4672165 0.01213767 0.1765839
## 195 195 9.711014 0.1955901 7.296778 0.4679040 0.01217577 0.1769962
## 196 196 9.711544 0.1955069 7.297111 0.4674341 0.01209792 0.1768215
## 197 197 9.711157 0.1955632 7.297203 0.4679034 0.01213014 0.1774002
## 198 198 9.711459 0.1955178 7.297382 0.4676873 0.01212118 0.1780176
## 199 199 9.711900 0.1954421 7.297893 0.4680823 0.01208655 0.1783009
## 200 200 9.712004 0.1954235 7.297919 0.4682057 0.01205710 0.1783415
## 201 201 9.711954 0.1954228 7.297856 0.4677251 0.01197920 0.1782884
## 202 202 9.711901 0.1954229 7.298340 0.4674532 0.01190788 0.1782757
## 203 203 9.712623 0.1953239 7.298382 0.4671891 0.01185634 0.1783254
## 204 204 9.712719 0.1953042 7.298505 0.4673183 0.01182433 0.1784031
## 205 205 9.712703 0.1953109 7.298014 0.4670963 0.01182599 0.1783063
## 206 206 9.712524 0.1953378 7.297391 0.4676790 0.01191285 0.1787110
## 207 207 9.712771 0.1953050 7.297171 0.4676780 0.01194307 0.1790044
## 208 208 9.712553 0.1953393 7.296363 0.4676571 0.01190078 0.1787989
## 209 209 9.712615 0.1953323 7.296752 0.4676331 0.01194507 0.1788300
## 210 210 9.713028 0.1952757 7.297286 0.4670797 0.01196909 0.1785525
## 211 211 9.712817 0.1953113 7.297561 0.4679047 0.01196891 0.1789645
## 212 212 9.713661 0.1951954 7.297866 0.4674915 0.01194017 0.1790801
## 213 213 9.714192 0.1951190 7.298356 0.4672243 0.01199485 0.1787955
## 214 214 9.713905 0.1951595 7.298138 0.4673039 0.01203417 0.1786011
## 215 215 9.714339 0.1950940 7.298358 0.4674120 0.01202189 0.1787510
## 216 216 9.714256 0.1951055 7.298302 0.4678542 0.01204842 0.1789006
## 217 217 9.714555 0.1950657 7.298322 0.4680558 0.01208133 0.1793217
## 218 218 9.714872 0.1950193 7.298600 0.4680072 0.01207305 0.1790553
## 219 219 9.715020 0.1949969 7.298801 0.4680128 0.01202056 0.1790669
## 220 220 9.715131 0.1949851 7.298787 0.4680137 0.01203149 0.1789404
## 221 221 9.714983 0.1950076 7.298457 0.4680670 0.01203679 0.1790190
## 222 222 9.715141 0.1949809 7.298526 0.4681280 0.01203892 0.1789291
## 223 223 9.715056 0.1949918 7.298249 0.4682563 0.01201705 0.1791098
## 224 224 9.715004 0.1949958 7.298306 0.4683078 0.01204532 0.1789677
## 225 225 9.714932 0.1950083 7.298194 0.4683754 0.01207181 0.1791277
## 226 226 9.714810 0.1950258 7.298019 0.4683111 0.01207395 0.1789807
## 227 227 9.714748 0.1950348 7.297978 0.4683425 0.01206339 0.1788580
## 228 228 9.714719 0.1950403 7.297953 0.4682105 0.01204776 0.1788258
## 229 229 9.714697 0.1950467 7.297814 0.4681191 0.01202929 0.1787875
## 230 230 9.714758 0.1950402 7.297953 0.4682279 0.01206153 0.1788916
## 231 231 9.714536 0.1950721 7.297934 0.4683308 0.01207297 0.1788853
## 232 232 9.714408 0.1950926 7.297743 0.4683593 0.01207440 0.1787876
## 233 233 9.714291 0.1951097 7.297615 0.4683927 0.01207864 0.1787479
## 234 234 9.714310 0.1951048 7.297683 0.4683408 0.01206610 0.1786733
## 235 235 9.714420 0.1950895 7.297781 0.4682275 0.01204521 0.1785377
## 236 236 9.714438 0.1950871 7.297812 0.4682926 0.01205669 0.1786077
## 237 237 9.714535 0.1950727 7.297864 0.4683203 0.01206595 0.1786126
## 238 238 9.714524 0.1950741 7.297823 0.4682732 0.01206230 0.1785109
## 239 239 9.714518 0.1950747 7.297805 0.4682435 0.01206008 0.1784736
## 240 240 9.714503 0.1950768 7.297804 0.4682653 0.01206096 0.1784811
## nvmax
## 19 19## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'## Coefficients of final model:
## (Intercept) x4 x7 x8 x9
## 8.941836e+01 -1.276249e-02 3.235631e+00 1.285802e-01 9.650356e-01
## x10 x11 x14 x16 x17
## 3.156375e-01 5.382116e+07 -2.523649e-01 2.760891e-01 4.401452e-01
## x21 stat13 stat14 stat24 stat60
## 3.914063e-02 -1.817820e-01 -2.758714e-01 -1.746312e-01 1.952430e-01
## stat98 stat110 stat144 stat149 sqrt.x18
## 9.490836e-01 -9.372953e-01 1.657180e-01 -2.076103e-01 7.619056e+00Test
if (algo.backward.caret == TRUE){
test.model(model.backward, data.test
,method = 'leapBackward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 109.1 121.9 125.5 125.3 129.0 140.3
## [1] "leapBackward Test MSE: 90.3031382273639"
Backward Elimination with CV (w/ filtered train)
Train
if (algo.backward.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train2
,method = "leapBackward"
,feature.names = feature.names)
model.backward = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 25 on full training set
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 8.270268 0.1500471 6.662698 0.1634449 0.02514052 0.11664558
## 2 2 7.968058 0.2109679 6.442396 0.1268344 0.02841881 0.10963931
## 3 3 7.845842 0.2351572 6.312228 0.1026749 0.02303243 0.08405260
## 4 4 7.665810 0.2697308 6.108489 0.1030712 0.02687427 0.08085558
## 5 5 7.567646 0.2882837 6.030670 0.1017884 0.02394369 0.06889467
## 6 6 7.533046 0.2946383 6.009967 0.1156649 0.02350019 0.07647690
## 7 7 7.535902 0.2941827 6.019534 0.1327010 0.02479979 0.08794715
## 8 8 7.508355 0.2992123 6.004663 0.1307841 0.02582231 0.07862328
## 9 9 7.494092 0.3018055 5.993913 0.1243981 0.02715968 0.06523736
## 10 10 7.462905 0.3076898 5.979216 0.1372392 0.02736091 0.07700172
## 11 11 7.458523 0.3084401 5.980278 0.1231068 0.02589088 0.07232327
## 12 12 7.449626 0.3101415 5.974128 0.1254919 0.02653904 0.07458857
## 13 13 7.454874 0.3092337 5.979360 0.1242300 0.02825630 0.07645168
## 14 14 7.453214 0.3095297 5.976030 0.1223252 0.02822013 0.07732297
## 15 15 7.444585 0.3111541 5.968770 0.1215171 0.02886534 0.07060026
## 16 16 7.443081 0.3114727 5.970313 0.1189044 0.02738134 0.06978336
## 17 17 7.438248 0.3122982 5.965056 0.1204191 0.02681958 0.07170486
## 18 18 7.439011 0.3122122 5.967540 0.1175664 0.02705692 0.06333219
## 19 19 7.442122 0.3115874 5.970148 0.1151504 0.02686571 0.06105625
## 20 20 7.444540 0.3111446 5.968736 0.1128034 0.02619355 0.06510858
## 21 21 7.440622 0.3118520 5.966512 0.1103750 0.02631120 0.06815638
## 22 22 7.442251 0.3115015 5.969164 0.1189506 0.02697655 0.07921281
## 23 23 7.437949 0.3123222 5.971178 0.1195624 0.02669437 0.08042746
## 24 24 7.434140 0.3130293 5.967030 0.1255552 0.02619411 0.08448472
## 25 25 7.427174 0.3142952 5.964074 0.1294530 0.02629751 0.08569100
## 26 26 7.431226 0.3135857 5.966708 0.1303466 0.02536487 0.08736138
## 27 27 7.427822 0.3142255 5.965260 0.1311610 0.02542720 0.09038605
## 28 28 7.429214 0.3139957 5.962745 0.1334063 0.02596286 0.09184781
## 29 29 7.431424 0.3135624 5.962761 0.1297904 0.02494089 0.08914026
## 30 30 7.441750 0.3117961 5.970501 0.1259454 0.02486100 0.08599562
## 31 31 7.445583 0.3111120 5.977874 0.1253871 0.02505912 0.09094178
## 32 32 7.446121 0.3110165 5.977999 0.1249858 0.02438610 0.09250046
## 33 33 7.445301 0.3111792 5.976954 0.1250273 0.02418400 0.09163260
## 34 34 7.446546 0.3109881 5.978967 0.1264497 0.02482255 0.09475348
## 35 35 7.441776 0.3118613 5.973790 0.1249731 0.02543126 0.09147111
## 36 36 7.440601 0.3120755 5.973329 0.1193922 0.02529089 0.08766689
## 37 37 7.441438 0.3119327 5.973926 0.1216543 0.02555754 0.09161323
## 38 38 7.441237 0.3119847 5.973344 0.1206545 0.02586364 0.09033567
## 39 39 7.443702 0.3115889 5.974059 0.1235022 0.02572046 0.09159439
## 40 40 7.444618 0.3114191 5.973027 0.1206947 0.02484132 0.08959653
## 41 41 7.443342 0.3116232 5.971038 0.1232758 0.02556667 0.08886533
## 42 42 7.447677 0.3108500 5.969916 0.1238124 0.02510430 0.09102123
## 43 43 7.447273 0.3109650 5.969148 0.1228627 0.02515700 0.08804876
## 44 44 7.450414 0.3104280 5.970952 0.1228812 0.02514916 0.08890584
## 45 45 7.453345 0.3099460 5.973643 0.1177915 0.02515479 0.08436014
## 46 46 7.453751 0.3099096 5.974773 0.1180242 0.02541496 0.08357601
## 47 47 7.453900 0.3099192 5.974828 0.1171634 0.02559531 0.08414982
## 48 48 7.460176 0.3088358 5.980846 0.1193960 0.02539359 0.08825626
## 49 49 7.458241 0.3091736 5.980240 0.1169120 0.02465835 0.08774326
## 50 50 7.458086 0.3092255 5.980311 0.1137444 0.02450535 0.08368574
## 51 51 7.460524 0.3088277 5.981566 0.1127413 0.02364404 0.08443702
## 52 52 7.465055 0.3080614 5.986789 0.1127399 0.02371416 0.08231407
## 53 53 7.465296 0.3080425 5.988935 0.1134049 0.02357415 0.08301551
## 54 54 7.472170 0.3068795 5.996714 0.1107544 0.02299286 0.08027537
## 55 55 7.475868 0.3062642 6.001846 0.1120293 0.02341960 0.08118716
## 56 56 7.473883 0.3066488 6.000088 0.1092365 0.02334091 0.07944026
## 57 57 7.471969 0.3070440 5.999743 0.1080261 0.02264240 0.07666770
## 58 58 7.475036 0.3065419 6.001151 0.1060680 0.02216629 0.07565391
## 59 59 7.472164 0.3070758 5.999577 0.1055306 0.02214947 0.07483212
## 60 60 7.474729 0.3066672 6.001527 0.1053836 0.02251541 0.07327837
## 61 61 7.478230 0.3060490 6.005019 0.1072885 0.02251058 0.07460191
## 62 62 7.480669 0.3056922 6.009906 0.1077276 0.02236505 0.07384589
## 63 63 7.481204 0.3056221 6.011057 0.1086292 0.02256147 0.07307206
## 64 64 7.480801 0.3057051 6.011347 0.1098353 0.02253913 0.07506009
## 65 65 7.479166 0.3060051 6.009918 0.1120246 0.02239136 0.07671213
## 66 66 7.480216 0.3057959 6.009439 0.1120182 0.02229617 0.07766787
## 67 67 7.478825 0.3060437 6.007099 0.1101808 0.02214942 0.07722189
## 68 68 7.480875 0.3056969 6.006979 0.1085868 0.02209887 0.07822039
## 69 69 7.484729 0.3050401 6.008843 0.1096969 0.02279888 0.07973403
## 70 70 7.480678 0.3057420 6.004861 0.1081265 0.02234294 0.07816393
## 71 71 7.483027 0.3053382 6.004790 0.1064108 0.02203522 0.07732623
## 72 72 7.482976 0.3053583 6.006413 0.1078810 0.02204946 0.07859592
## 73 73 7.482595 0.3054271 6.005388 0.1059319 0.02201453 0.07661897
## 74 74 7.483837 0.3052251 6.005435 0.1049521 0.02197694 0.07598431
## 75 75 7.484748 0.3050567 6.006019 0.1064646 0.02162645 0.07539546
## 76 76 7.487586 0.3045650 6.007583 0.1054888 0.02136606 0.07624709
## 77 77 7.487752 0.3045423 6.009507 0.1081814 0.02222531 0.07730344
## 78 78 7.490005 0.3041802 6.011585 0.1124504 0.02200105 0.08274354
## 79 79 7.493171 0.3036050 6.013108 0.1159944 0.02228666 0.08201694
## 80 80 7.493554 0.3035575 6.013235 0.1152690 0.02239749 0.08072814
## 81 81 7.492880 0.3037017 6.012753 0.1162927 0.02304598 0.08118578
## 82 82 7.493149 0.3036770 6.014960 0.1148346 0.02314136 0.08028994
## 83 83 7.493816 0.3035515 6.015127 0.1130597 0.02253932 0.07954361
## 84 84 7.498473 0.3027360 6.018249 0.1110006 0.02237901 0.07653606
## 85 85 7.502141 0.3021105 6.020967 0.1099354 0.02245952 0.07610001
## 86 86 7.501710 0.3021672 6.019673 0.1095919 0.02262022 0.07665509
## 87 87 7.501871 0.3021578 6.021237 0.1099596 0.02307588 0.07576896
## 88 88 7.502050 0.3021357 6.021830 0.1087324 0.02287321 0.07358517
## 89 89 7.504912 0.3016265 6.024632 0.1077560 0.02287624 0.07214764
## 90 90 7.506408 0.3014081 6.023257 0.1098940 0.02312486 0.07332067
## 91 91 7.506526 0.3014133 6.024656 0.1095343 0.02357754 0.07072056
## 92 92 7.506693 0.3013937 6.025015 0.1086677 0.02342937 0.06887131
## 93 93 7.506026 0.3014844 6.024724 0.1089327 0.02271143 0.06977705
## 94 94 7.506865 0.3013203 6.026430 0.1103625 0.02292282 0.07067471
## 95 95 7.508889 0.3009854 6.028271 0.1113812 0.02331627 0.07214292
## 96 96 7.510282 0.3007904 6.029589 0.1128518 0.02308720 0.07422661
## 97 97 7.509852 0.3008828 6.027797 0.1130944 0.02323827 0.07510239
## 98 98 7.511941 0.3005554 6.028083 0.1163155 0.02348072 0.07699452
## 99 99 7.513392 0.3003125 6.028237 0.1168269 0.02334660 0.07779947
## 100 100 7.515310 0.3000093 6.029965 0.1157923 0.02370533 0.07486987
## 101 101 7.517200 0.2997267 6.032006 0.1146205 0.02350807 0.07227026
## 102 102 7.518523 0.2995250 6.034009 0.1135190 0.02324764 0.07042455
## 103 103 7.517254 0.2997201 6.032226 0.1113667 0.02309362 0.06870833
## 104 104 7.515245 0.3000877 6.032112 0.1116959 0.02298904 0.06845710
## 105 105 7.514488 0.3002056 6.032143 0.1102818 0.02299985 0.06923370
## 106 106 7.515067 0.3001279 6.033007 0.1099899 0.02293756 0.07029180
## 107 107 7.514177 0.3003133 6.033009 0.1109935 0.02279674 0.07224012
## 108 108 7.514110 0.3003185 6.032724 0.1114591 0.02293613 0.07192700
## 109 109 7.513273 0.3004550 6.032354 0.1106316 0.02278757 0.07034276
## 110 110 7.511385 0.3007876 6.029884 0.1110685 0.02257911 0.06984393
## 111 111 7.512485 0.3006073 6.030798 0.1111834 0.02292981 0.07004785
## 112 112 7.513823 0.3003851 6.032090 0.1093669 0.02274687 0.06820350
## 113 113 7.512365 0.3006401 6.029321 0.1087288 0.02267028 0.06706054
## 114 114 7.512264 0.3006559 6.028617 0.1084646 0.02251325 0.06774419
## 115 115 7.512725 0.3005805 6.027650 0.1083601 0.02292224 0.06639176
## 116 116 7.511498 0.3008008 6.027000 0.1112489 0.02290050 0.06868617
## 117 117 7.512270 0.3006845 6.028793 0.1100459 0.02267588 0.06752702
## 118 118 7.513411 0.3005039 6.029214 0.1098004 0.02267395 0.06762526
## 119 119 7.513604 0.3004762 6.028007 0.1066377 0.02237542 0.06540439
## 120 120 7.514593 0.3003166 6.028372 0.1042153 0.02200413 0.06420850
## 121 121 7.513811 0.3004596 6.027903 0.1025283 0.02191642 0.06192917
## 122 122 7.515258 0.3001949 6.029880 0.1014389 0.02170668 0.06040279
## 123 123 7.517332 0.2998595 6.031000 0.1034072 0.02210530 0.06063177
## 124 124 7.515873 0.3001221 6.030761 0.1009483 0.02166475 0.06067485
## 125 125 7.515610 0.3001808 6.029782 0.1006348 0.02161850 0.05981324
## 126 126 7.515092 0.3003109 6.029855 0.1026545 0.02154195 0.06063064
## 127 127 7.514734 0.3003767 6.029924 0.1015919 0.02133530 0.06094845
## 128 128 7.515041 0.3003212 6.029430 0.1019733 0.02143998 0.06161469
## 129 129 7.513366 0.3006122 6.027302 0.1017597 0.02129756 0.06132643
## 130 130 7.515584 0.3002402 6.029337 0.1013127 0.02134548 0.05896629
## 131 131 7.517034 0.3000146 6.029808 0.1022771 0.02137029 0.06021820
## 132 132 7.517722 0.2998931 6.030466 0.1017135 0.02143542 0.05905746
## 133 133 7.517219 0.2999718 6.029875 0.1005374 0.02119156 0.05828640
## 134 134 7.516902 0.3000405 6.029788 0.1012673 0.02132374 0.05973755
## 135 135 7.517124 0.3000102 6.029411 0.1013392 0.02109470 0.06041697
## 136 136 7.518035 0.2998729 6.031110 0.1013875 0.02102385 0.06057422
## 137 137 7.517644 0.2999498 6.030696 0.1020740 0.02097237 0.06183591
## 138 138 7.516270 0.3001766 6.029339 0.1029455 0.02087318 0.06193984
## 139 139 7.515536 0.3003313 6.028896 0.1034838 0.02073209 0.06282060
## 140 140 7.516923 0.3000842 6.030539 0.1036188 0.02066566 0.06372622
## 141 141 7.518062 0.2998865 6.031149 0.1025970 0.02053860 0.06440622
## 142 142 7.518806 0.2997621 6.032485 0.1021684 0.02040639 0.06409613
## 143 143 7.518464 0.2998224 6.032120 0.1026156 0.02039682 0.06518039
## 144 144 7.518539 0.2998196 6.031555 0.1028399 0.02074333 0.06432711
## 145 145 7.518937 0.2997566 6.031384 0.1012382 0.02052701 0.06247393
## 146 146 7.519216 0.2997125 6.031307 0.1019752 0.02055811 0.06312701
## 147 147 7.518230 0.2998780 6.029872 0.1033369 0.02063772 0.06328403
## 148 148 7.519361 0.2996896 6.031070 0.1035790 0.02065816 0.06423716
## 149 149 7.520784 0.2994414 6.032792 0.1031724 0.02045969 0.06319620
## 150 150 7.519248 0.2997089 6.031132 0.1031322 0.02040693 0.06354567
## 151 151 7.521098 0.2993892 6.032277 0.1037411 0.02041624 0.06446269
## 152 152 7.520753 0.2994599 6.032190 0.1042047 0.02033006 0.06536267
## 153 153 7.520357 0.2995502 6.031942 0.1049055 0.02030479 0.06626183
## 154 154 7.520715 0.2995027 6.031811 0.1061949 0.02028820 0.06696120
## 155 155 7.521349 0.2994028 6.032584 0.1061160 0.02031935 0.06610253
## 156 156 7.521916 0.2992910 6.033409 0.1071405 0.02036008 0.06710464
## 157 157 7.522612 0.2991837 6.033967 0.1073542 0.02050710 0.06709202
## 158 158 7.522700 0.2991697 6.033912 0.1080933 0.02077781 0.06795445
## 159 159 7.522539 0.2991862 6.033806 0.1087128 0.02087151 0.06764647
## 160 160 7.522835 0.2991363 6.033007 0.1077427 0.02068118 0.06719252
## 161 161 7.522430 0.2992031 6.032445 0.1083875 0.02070690 0.06671580
## 162 162 7.521755 0.2993230 6.032380 0.1078345 0.02059563 0.06668156
## 163 163 7.521093 0.2994595 6.031561 0.1088158 0.02054414 0.06740983
## 164 164 7.518880 0.2998390 6.030391 0.1091655 0.02047308 0.06811904
## 165 165 7.517715 0.3000240 6.030372 0.1088889 0.02053331 0.06809058
## 166 166 7.518001 0.2999859 6.030802 0.1084778 0.02050835 0.06793515
## 167 167 7.519552 0.2997066 6.032801 0.1073626 0.02062842 0.06714816
## 168 168 7.519574 0.2997032 6.033045 0.1071907 0.02063203 0.06669179
## 169 169 7.518869 0.2998312 6.032718 0.1080092 0.02070083 0.06769471
## 170 170 7.519362 0.2997504 6.033046 0.1071654 0.02043690 0.06729498
## 171 171 7.518966 0.2998156 6.032863 0.1069015 0.02037225 0.06632514
## 172 172 7.519354 0.2997416 6.033477 0.1066949 0.02036840 0.06608949
## 173 173 7.518632 0.2998615 6.032624 0.1065785 0.02034063 0.06613347
## 174 174 7.518506 0.2998816 6.032835 0.1060191 0.02040943 0.06594469
## 175 175 7.518397 0.2998959 6.032399 0.1065667 0.02032326 0.06577087
## 176 176 7.518452 0.2998750 6.032629 0.1065201 0.02012604 0.06675669
## 177 177 7.518141 0.2999341 6.033538 0.1060704 0.02000567 0.06711064
## 178 178 7.517356 0.3000801 6.033049 0.1066418 0.02012656 0.06711536
## 179 179 7.516744 0.3001918 6.032558 0.1063481 0.02009002 0.06705939
## 180 180 7.517322 0.3000978 6.033476 0.1063932 0.02006960 0.06663227
## 181 181 7.517367 0.3000828 6.033366 0.1061341 0.01991936 0.06640776
## 182 182 7.517600 0.3000466 6.033933 0.1056425 0.01996062 0.06635790
## 183 183 7.517268 0.3000974 6.033610 0.1055384 0.01979285 0.06668004
## 184 184 7.516774 0.3001848 6.033570 0.1062547 0.01986365 0.06743086
## 185 185 7.516689 0.3002131 6.033869 0.1054772 0.02005163 0.06577075
## 186 186 7.516927 0.3001668 6.033719 0.1058825 0.02000351 0.06605502
## 187 187 7.517304 0.3001067 6.034072 0.1057429 0.01987918 0.06598830
## 188 188 7.518114 0.2999695 6.034718 0.1049532 0.01974031 0.06547362
## 189 189 7.517413 0.3000919 6.034375 0.1050130 0.01971793 0.06537223
## 190 190 7.517130 0.3001269 6.034653 0.1044322 0.01969764 0.06496985
## 191 191 7.516484 0.3002316 6.034155 0.1042314 0.01971705 0.06426306
## 192 192 7.516329 0.3002585 6.034149 0.1042962 0.01971048 0.06399616
## 193 193 7.516271 0.3002687 6.034142 0.1038466 0.01971664 0.06381055
## 194 194 7.516278 0.3002744 6.033669 0.1042874 0.01972904 0.06437953
## 195 195 7.515962 0.3003362 6.032721 0.1042528 0.01983218 0.06438916
## 196 196 7.516237 0.3002949 6.033204 0.1047050 0.01990886 0.06406693
## 197 197 7.515725 0.3003818 6.032604 0.1041790 0.01979505 0.06353693
## 198 198 7.516321 0.3002861 6.032834 0.1044986 0.01975255 0.06399512
## 199 199 7.515594 0.3004068 6.032229 0.1044989 0.01976125 0.06389486
## 200 200 7.516076 0.3003225 6.032670 0.1044995 0.01980328 0.06327669
## 201 201 7.516390 0.3002663 6.032982 0.1041519 0.01972846 0.06378889
## 202 202 7.516036 0.3003287 6.032685 0.1037726 0.01982285 0.06308160
## 203 203 7.515731 0.3003807 6.032575 0.1040710 0.01975302 0.06362317
## 204 204 7.515598 0.3004055 6.032077 0.1037319 0.01971876 0.06337082
## 205 205 7.515233 0.3004672 6.031563 0.1038177 0.01976092 0.06353169
## 206 206 7.515352 0.3004440 6.031727 0.1043152 0.01973340 0.06379095
## 207 207 7.515428 0.3004288 6.031680 0.1047298 0.01972795 0.06435322
## 208 208 7.515083 0.3004870 6.031357 0.1044821 0.01969237 0.06448936
## 209 209 7.515555 0.3004112 6.031945 0.1038538 0.01960536 0.06439284
## 210 210 7.515583 0.3004160 6.032081 0.1034344 0.01962462 0.06400060
## 211 211 7.514964 0.3005245 6.031261 0.1033488 0.01962963 0.06386220
## 212 212 7.515225 0.3004823 6.031637 0.1030677 0.01970532 0.06369830
## 213 213 7.514648 0.3005807 6.030924 0.1026866 0.01968761 0.06341523
## 214 214 7.514046 0.3006847 6.030390 0.1026815 0.01971050 0.06334877
## 215 215 7.514162 0.3006612 6.030339 0.1027709 0.01970342 0.06317489
## 216 216 7.514219 0.3006512 6.030363 0.1028697 0.01966107 0.06327584
## 217 217 7.513932 0.3007048 6.030002 0.1030286 0.01965270 0.06324843
## 218 218 7.513932 0.3007022 6.029944 0.1027652 0.01964202 0.06297415
## 219 219 7.513788 0.3007318 6.029779 0.1026667 0.01964564 0.06278031
## 220 220 7.513925 0.3007077 6.029979 0.1024915 0.01960282 0.06292582
## 221 221 7.514146 0.3006688 6.030109 0.1026152 0.01965349 0.06257690
## 222 222 7.514234 0.3006541 6.029996 0.1025941 0.01961279 0.06247693
## 223 223 7.513945 0.3007056 6.029742 0.1026614 0.01961009 0.06258606
## 224 224 7.513930 0.3007118 6.029786 0.1026362 0.01964959 0.06254641
## 225 225 7.513770 0.3007401 6.029577 0.1024963 0.01962453 0.06260621
## 226 226 7.513661 0.3007630 6.029545 0.1026501 0.01968100 0.06263315
## 227 227 7.513658 0.3007620 6.029612 0.1024835 0.01965718 0.06261198
## 228 228 7.513582 0.3007738 6.029623 0.1024718 0.01966532 0.06256661
## 229 229 7.513521 0.3007838 6.029502 0.1020795 0.01965917 0.06235755
## 230 230 7.513227 0.3008357 6.029330 0.1021693 0.01964450 0.06254157
## 231 231 7.513332 0.3008164 6.029465 0.1021261 0.01962689 0.06255784
## 232 232 7.513532 0.3007804 6.029636 0.1020927 0.01962129 0.06254178
## 233 233 7.513489 0.3007880 6.029626 0.1020469 0.01962357 0.06249576
## 234 234 7.513532 0.3007808 6.029729 0.1020161 0.01962047 0.06254948
## 235 235 7.513564 0.3007764 6.029752 0.1019786 0.01963529 0.06253389
## 236 236 7.513592 0.3007697 6.029811 0.1019815 0.01962200 0.06254947
## 237 237 7.513596 0.3007691 6.029771 0.1019959 0.01961401 0.06255203
## 238 238 7.513563 0.3007753 6.029785 0.1018913 0.01961497 0.06243028
## 239 239 7.513563 0.3007754 6.029787 0.1019127 0.01962115 0.06241481
## 240 240 7.513584 0.3007718 6.029796 0.1019202 0.01962246 0.06241429
## nvmax
## 25 25## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'## Coefficients of final model:
## (Intercept) x4 x7 x8 x9
## 8.733025e+01 -1.487732e-02 3.352477e+00 1.410604e-01 9.451043e-01
## x10 x11 x16 x17 x21
## 4.253677e-01 5.771201e+07 2.555669e-01 4.181964e-01 3.566003e-02
## stat4 stat13 stat14 stat23 stat25
## -1.636272e-01 -1.831055e-01 -3.085334e-01 1.948212e-01 -1.437340e-01
## stat38 stat41 stat60 stat85 stat98
## 1.589337e-01 -1.702179e-01 1.948465e-01 -1.431581e-01 8.584054e-01
## stat110 stat128 stat144 stat146 stat149
## -8.961450e-01 -1.604357e-01 1.596797e-01 -1.498132e-01 -2.043875e-01
## sqrt.x18
## 7.454872e+00Test
if (algo.backward.caret == TRUE){
test.model(model.backward, data.test
,method = 'leapBackward',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 107.3 120.7 124.3 124.1 127.8 138.1
## [1] "leapBackward Test MSE: 91.2164226586688"
Stepwise Selection (w/ full train)
Train
if (algo.stepwise == TRUE){
t1 = Sys.time()
model.stepwise = step(model.null, scope=list(upper=model.full), data = data.train, direction="both", trace = 0)
print(summary(model.stepwise))
#saveRDS(model.stepwise,file = "model_stepwise.rds")
t2 = Sys.time()
print (paste("Time taken for Stepwise Selection: ",t2-t1, sep = ""))
plot.diagnostics(model.stepwise, data.train)
}Test
if (algo.stepwise == TRUE){
test.model(model.stepwise, data.test, "Stepwise Selection")
}Stepwise Selection (w/ filtered train)
Train
if (algo.stepwise == TRUE){
t1 = Sys.time()
model.stepwise2 = step(model.null2, scope=list(upper=model.full2), data = data.train2, direction="both", trace = 0)
print(summary(model.stepwise2))
#saveRDS(model.forward,file = "model_stepwise.rds")
t2 = Sys.time()
print (paste("Time taken for Stepwise Selection: ",t2-t1, sep = ""))
plot.diagnostics(model.stepwise2, data.train2)
}Test
if (algo.stepwise == TRUE){
test.model(model.stepwise2, data.test, "Stepwise Selection (2)")
}Stepwise Selection with CV (w/ full train)
Train
if (algo.stepwise.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "leapSeq"
,feature.names = feature.names)
model.stepwise = returned$model
id = returned$id
}## Aggregating results
## Selecting tuning parameters
## Fitting nvmax = 19 on full training set
## nvmax RMSE Rsquared MAE RMSESD RsquaredSD MAESD
## 1 1 10.205848 0.1070230 7.793298 0.4837937 0.02121144 0.2343155
## 2 2 9.978578 0.1456242 7.594919 0.4865059 0.01542500 0.2210630
## 3 3 9.869319 0.1645156 7.472217 0.4757917 0.01700325 0.2032220
## 4 4 9.705345 0.1918124 7.255723 0.4773872 0.01219753 0.1920870
## 5 5 9.623121 0.2056678 7.191041 0.5001426 0.01530975 0.2093101
## 6 6 9.615614 0.2067906 7.190418 0.4962592 0.01340840 0.1969631
## 7 7 9.599094 0.2094876 7.178668 0.4953228 0.01391436 0.2006617
## 8 8 9.581185 0.2124654 7.171670 0.4983385 0.01423833 0.2054035
## 9 9 9.573978 0.2136032 7.160477 0.4946051 0.01182847 0.1967355
## 10 10 9.566457 0.2148079 7.156153 0.4890367 0.01057451 0.1936818
## 11 11 9.567690 0.2147292 7.159764 0.4979287 0.01271238 0.2087616
## 12 12 9.572535 0.2139549 7.164093 0.4913304 0.01123655 0.2012837
## 13 13 9.571512 0.2141605 7.161750 0.4913776 0.01141375 0.1948090
## 14 14 9.667172 0.1966716 7.239365 0.3651035 0.04963529 0.2150276
## 15 15 9.568774 0.2146047 7.157827 0.4818420 0.01068948 0.1909961
## 16 16 9.565261 0.2152305 7.160380 0.4895184 0.01216199 0.1976081
## 17 17 9.567334 0.2149625 7.164737 0.4913768 0.01360563 0.2009011
## 18 18 9.572223 0.2142536 7.165375 0.4935820 0.01405113 0.2001792
## 19 19 9.562362 0.2158963 7.158834 0.4926740 0.01415188 0.2033848
## 20 20 9.754853 0.1831328 7.325915 0.6508972 0.07112079 0.4009606
## 21 21 9.667648 0.1990850 7.242520 0.7172097 0.05305699 0.4266902
## 22 22 9.571406 0.2145969 7.160732 0.4957266 0.01458413 0.2060193
## 23 23 9.660007 0.1996663 7.233095 0.6284673 0.05219118 0.3544183
## 24 24 9.583368 0.2127542 7.167614 0.4983340 0.01469583 0.2017528
## 25 25 9.677466 0.1954907 7.242970 0.3686926 0.04851463 0.2016169
## 26 26 9.583743 0.2127369 7.164793 0.4979161 0.01452431 0.1991570
## 27 27 9.587283 0.2122448 7.169803 0.4930287 0.01371925 0.1929269
## 28 28 9.665424 0.1988109 7.255504 0.5428599 0.04478033 0.3168007
## 29 29 9.673551 0.1975585 7.255762 0.5365232 0.04296156 0.3206129
## 30 30 9.661499 0.1992733 7.243027 0.4643831 0.03493555 0.2650344
## 31 31 9.761705 0.1833666 7.339327 0.7342722 0.06364207 0.4725557
## 32 32 9.595537 0.2109734 7.183650 0.4915331 0.01370418 0.1941739
## 33 33 9.668088 0.1982384 7.247809 0.4559111 0.03433277 0.2554943
## 34 34 9.692269 0.1943600 7.260484 0.5478561 0.05158621 0.2957152
## 35 35 9.691701 0.1946775 7.266045 0.5572802 0.05041756 0.2596346
## 36 36 9.710728 0.1926632 7.275616 0.6944079 0.04993792 0.4066353
## 37 37 9.890349 0.1622596 7.439056 0.8238863 0.07486707 0.5032664
## 38 38 9.623849 0.2066853 7.201725 0.4821647 0.01334456 0.1844175
## 39 39 9.697088 0.1939183 7.265840 0.5488092 0.04829880 0.2472763
## 40 40 9.806936 0.1765717 7.360640 0.7799452 0.06637559 0.4824487
## 41 41 9.890229 0.1612827 7.444983 0.6939056 0.07524574 0.3823510
## 42 42 9.791108 0.1783603 7.361201 0.6371773 0.05908595 0.4041515
## 43 43 9.630017 0.2057897 7.208405 0.4964906 0.01402942 0.1992664
## 44 44 9.632903 0.2054327 7.213008 0.4954107 0.01434914 0.1968310
## 45 45 9.789790 0.1771470 7.346855 0.3101937 0.05186585 0.2363741
## 46 46 9.698911 0.1938891 7.287534 0.5436979 0.04441081 0.3185793
## 47 47 9.714252 0.1917306 7.284569 0.6234033 0.05090673 0.3391275
## 48 48 9.796262 0.1778664 7.365890 0.6931181 0.06419081 0.3644622
## 49 49 9.767536 0.1816998 7.338819 0.5298542 0.05387138 0.2881042
## 50 50 9.637942 0.2048147 7.226843 0.4913799 0.01284409 0.1944797
## 51 51 9.866829 0.1639003 7.421309 0.3693511 0.06253153 0.2425638
## 52 52 9.642579 0.2040996 7.229097 0.4891556 0.01254095 0.1929687
## 53 53 9.647751 0.2033738 7.233073 0.4870160 0.01192579 0.1912024
## 54 54 9.841854 0.1690102 7.435294 0.5220489 0.05574156 0.3790380
## 55 55 9.890808 0.1624887 7.459213 0.7518592 0.07222948 0.4697268
## 56 56 9.704218 0.1931139 7.290025 0.4706846 0.03202974 0.2534636
## 57 57 9.828787 0.1734083 7.383273 0.7311806 0.06518489 0.4472805
## 58 58 9.651134 0.2030893 7.236450 0.4907549 0.01232460 0.1966152
## 59 59 9.775628 0.1807208 7.364195 0.4938917 0.04466065 0.3269575
## 60 60 9.654436 0.2025888 7.239809 0.4903490 0.01308315 0.1950564
## 61 61 9.800132 0.1771332 7.369460 0.5606545 0.05519135 0.3325896
## 62 62 9.744382 0.1869204 7.316264 0.5297419 0.05234565 0.2862918
## 63 63 9.655512 0.2025883 7.240903 0.4862989 0.01244579 0.1916203
## 64 64 9.654732 0.2027191 7.238955 0.4870720 0.01212953 0.1913291
## 65 65 9.653792 0.2029008 7.240310 0.4892313 0.01245258 0.1930654
## 66 66 9.658758 0.2021530 7.245213 0.4881657 0.01252597 0.1917628
## 67 67 9.658104 0.2022354 7.245916 0.4866751 0.01277515 0.1906355
## 68 68 9.877433 0.1645466 7.451598 0.6966835 0.06504695 0.4641528
## 69 69 9.742879 0.1879545 7.313709 0.6190560 0.05112852 0.3344059
## 70 70 9.657104 0.2024695 7.243922 0.4869482 0.01329759 0.1931608
## 71 71 9.884169 0.1635219 7.449931 0.6887683 0.06623845 0.3837369
## 72 72 9.821163 0.1744610 7.386343 0.6494693 0.06401674 0.3985422
## 73 73 9.813806 0.1745117 7.382073 0.3824512 0.05442309 0.2737273
## 74 74 9.813123 0.1756336 7.368114 0.6595856 0.06529523 0.3603530
## 75 75 9.715944 0.1915015 7.299077 0.4584832 0.03148521 0.2415375
## 76 76 9.658705 0.2023136 7.240721 0.4829924 0.01263009 0.1906733
## 77 77 9.816682 0.1745982 7.378859 0.5700113 0.06508182 0.3083729
## 78 78 9.753947 0.1871649 7.323583 0.7050405 0.05219045 0.4103875
## 79 79 9.728757 0.1899913 7.303279 0.5450891 0.04613288 0.2410723
## 80 80 9.657542 0.2025750 7.245793 0.4857156 0.01273750 0.1928025
## 81 81 9.875736 0.1643392 7.430484 0.5975809 0.06783743 0.3514538
## 82 82 9.661027 0.2021217 7.246509 0.4824492 0.01231761 0.1908359
## 83 83 9.747245 0.1876104 7.317907 0.6211392 0.05231599 0.3389481
## 84 84 9.750423 0.1865795 7.327886 0.5199529 0.05064731 0.2848899
## 85 85 9.662660 0.2019061 7.249560 0.4788297 0.01199038 0.1905972
## 86 86 9.755824 0.1857785 7.328905 0.5204940 0.05021701 0.2858548
## 87 87 9.825018 0.1744072 7.383505 0.6758154 0.06097878 0.3358698
## 88 88 9.836495 0.1720800 7.393056 0.6312501 0.06677987 0.3781959
## 89 89 9.759581 0.1861893 7.332083 0.6453826 0.04794514 0.3308907
## 90 90 10.052085 0.1348123 7.589378 0.7572040 0.07491613 0.5068181
## 91 91 9.742232 0.1883245 7.325446 0.5370037 0.04572747 0.3034232
## 92 92 9.745429 0.1878826 7.325927 0.5356700 0.04555989 0.3039753
## 93 93 9.807475 0.1759672 7.373610 0.5101272 0.05470393 0.3053785
## 94 94 9.726723 0.1899786 7.309848 0.4556845 0.03492317 0.2468652
## 95 95 9.825810 0.1744529 7.397533 0.6588187 0.05686335 0.3788034
## 96 96 9.991005 0.1462823 7.538621 0.7693476 0.07852728 0.4470752
## 97 97 9.747529 0.1874954 7.314033 0.5454636 0.04863922 0.2800521
## 98 98 9.669063 0.2012139 7.253637 0.4850862 0.01340729 0.1900389
## 99 99 9.746222 0.1878342 7.329376 0.5331434 0.04547075 0.3045927
## 100 100 9.859667 0.1679995 7.408045 0.3830575 0.06404970 0.2594193
## 101 101 9.756963 0.1864437 7.327139 0.6171725 0.05169535 0.3399277
## 102 102 9.866159 0.1683681 7.419355 0.5995406 0.06374656 0.3905077
## 103 103 9.756182 0.1863035 7.323709 0.5397656 0.04809870 0.2747757
## 104 104 9.756905 0.1862035 7.327747 0.5367317 0.04806866 0.2732414
## 105 105 9.761557 0.1858510 7.334476 0.6138594 0.05195081 0.3349864
## 106 106 9.775841 0.1845493 7.351114 0.6989651 0.05141410 0.4106269
## 107 107 9.679809 0.1997502 7.267562 0.4782268 0.01318868 0.1801019
## 108 108 9.851841 0.1708671 7.428944 0.6709641 0.06122359 0.3837901
## 109 109 9.929924 0.1562708 7.466421 0.5409825 0.07368042 0.3253191
## 110 110 9.764762 0.1851014 7.334885 0.5363624 0.04762464 0.2666889
## 111 111 9.970696 0.1515506 7.512362 0.7100552 0.07166214 0.4430499
## 112 112 9.769186 0.1848721 7.337602 0.6155445 0.05245223 0.3339394
## 113 113 9.685401 0.1990069 7.269797 0.4747922 0.01218572 0.1776034
## 114 114 9.787946 0.1823924 7.360639 0.6419216 0.04783109 0.3208396
## 115 115 9.766309 0.1849324 7.335572 0.5310433 0.04752834 0.2671718
## 116 116 9.861110 0.1687604 7.413185 0.5586921 0.06530423 0.3351105
## 117 117 9.784356 0.1834331 7.359182 0.6954412 0.05115998 0.4159221
## 118 118 9.849787 0.1717067 7.425200 0.7062931 0.05861239 0.4513249
## 119 119 9.859216 0.1685619 7.419631 0.3957168 0.06058269 0.2794490
## 120 120 9.690980 0.1982116 7.275868 0.4768088 0.01293721 0.1818628
## 121 121 9.767241 0.1857791 7.344439 0.5962003 0.03684435 0.2809068
## 122 122 9.761526 0.1863279 7.328946 0.5791071 0.04462824 0.2979247
## 123 123 9.694173 0.1977654 7.276088 0.4678762 0.01249599 0.1766908
## 124 124 9.814544 0.1782304 7.404891 0.6571133 0.04592424 0.4169079
## 125 125 9.847651 0.1721860 7.413361 0.6197523 0.05146462 0.3203784
## 126 126 9.839247 0.1736511 7.413600 0.6272760 0.05186607 0.3082046
## 127 127 9.860500 0.1702002 7.423877 0.5635256 0.05473517 0.3761397
## 128 128 9.760794 0.1864238 7.341018 0.5297653 0.04316311 0.2495953
## 129 129 9.796126 0.1801342 7.391755 0.5137713 0.04135545 0.3114097
## 130 130 9.699521 0.1970318 7.281778 0.4743573 0.01347134 0.1858399
## 131 131 9.778457 0.1842348 7.354999 0.5936856 0.03688326 0.2851011
## 132 132 9.766839 0.1852907 7.330135 0.3629290 0.03332878 0.1500760
## 133 133 9.741611 0.1895484 7.320819 0.5036780 0.03372860 0.2136497
## 134 134 9.784364 0.1827947 7.365090 0.5599019 0.02983182 0.2608973
## 135 135 9.827382 0.1763932 7.398617 0.6476484 0.04838620 0.3886404
## 136 136 9.765519 0.1854801 7.328292 0.3633627 0.03385954 0.1496003
## 137 137 9.796429 0.1814719 7.377846 0.6352224 0.04078433 0.3737992
## 138 138 9.696567 0.1975065 7.277658 0.4713338 0.01298252 0.1799341
## 139 139 9.728682 0.1910649 7.326020 0.4469149 0.01952404 0.2101222
## 140 140 9.696939 0.1974802 7.275982 0.4713972 0.01280562 0.1814833
## 141 141 9.807709 0.1789570 7.398235 0.6213568 0.04167252 0.3728498
## 142 142 9.778063 0.1824574 7.373620 0.4788266 0.03602759 0.2291808
## 143 143 9.766119 0.1854037 7.329698 0.3633686 0.03431011 0.1543842
## 144 144 9.831968 0.1741302 7.382998 0.3761801 0.04735865 0.2165069
## 145 145 9.760066 0.1872743 7.337412 0.5626570 0.02892796 0.2467934
## 146 146 9.833161 0.1739647 7.385352 0.3754350 0.04726298 0.2159764
## 147 147 9.697506 0.1974042 7.280452 0.4738620 0.01315596 0.1829651
## 148 148 9.934149 0.1582350 7.491004 0.7184225 0.06175763 0.4238277
## 149 149 9.698719 0.1972338 7.280051 0.4754688 0.01315388 0.1836875
## 150 150 9.699335 0.1971567 7.280477 0.4742080 0.01306974 0.1812704
## 151 151 9.765558 0.1858045 7.334896 0.4941589 0.03907042 0.2477996
## 152 152 9.764956 0.1865759 7.339577 0.5631708 0.02888641 0.2447091
## 153 153 9.766799 0.1857046 7.336009 0.5069329 0.03739074 0.2342680
## 154 154 9.759247 0.1870975 7.337645 0.5023504 0.03502383 0.2476759
## 155 155 9.703651 0.1965721 7.284149 0.4740852 0.01306864 0.1814425
## 156 156 9.768743 0.1860513 7.344447 0.5669928 0.02928693 0.2499670
## 157 157 9.864808 0.1683860 7.420514 0.3688602 0.04660355 0.2287535
## 158 158 9.705838 0.1962884 7.287443 0.4765856 0.01304326 0.1847617
## 159 159 9.958070 0.1533992 7.497965 0.4789394 0.05236824 0.2404793
## 160 160 9.823952 0.1766288 7.395495 0.5907209 0.04159159 0.2651377
## 161 161 9.739994 0.1894800 7.337710 0.4525122 0.02016262 0.2124322
## 162 162 9.769925 0.1858826 7.346586 0.5674685 0.02918956 0.2509198
## 163 163 9.851152 0.1710184 7.424737 0.5304903 0.04765679 0.2636172
## 164 164 9.705675 0.1962615 7.288091 0.4750686 0.01285978 0.1824472
## 165 165 9.843073 0.1726173 7.393228 0.3783518 0.04738197 0.2168783
## 166 166 9.706242 0.1962186 7.289184 0.4746018 0.01268388 0.1807184
## 167 167 9.859935 0.1702429 7.439882 0.5770360 0.04063988 0.2988954
## 168 168 9.707296 0.1960547 7.290261 0.4731732 0.01278193 0.1798009
## 169 169 9.797973 0.1797001 7.394705 0.4752098 0.03632498 0.2588401
## 170 170 9.801850 0.1800602 7.385451 0.5618091 0.03069719 0.2678155
## 171 171 9.708704 0.1959023 7.291018 0.4738181 0.01301194 0.1806541
## 172 172 9.777277 0.1843583 7.348222 0.4947615 0.03963994 0.2493232
## 173 173 9.948396 0.1541421 7.505768 0.3469153 0.05176332 0.2296520
## 174 174 9.708264 0.1959788 7.293230 0.4725473 0.01267767 0.1803379
## 175 175 9.799954 0.1804210 7.386034 0.5560915 0.02951421 0.2630787
## 176 176 9.710007 0.1957396 7.294215 0.4718303 0.01251621 0.1797027
## 177 177 9.709761 0.1957814 7.293598 0.4721962 0.01249503 0.1800756
## 178 178 9.709899 0.1957841 7.294202 0.4724907 0.01243319 0.1799258
## 179 179 9.710154 0.1957548 7.294527 0.4718398 0.01235600 0.1799241
## 180 180 9.901042 0.1635531 7.452728 0.4791869 0.04654934 0.2355561
## 181 181 9.711441 0.1955796 7.295954 0.4727161 0.01250022 0.1808782
## 182 182 9.781191 0.1838685 7.353476 0.4951686 0.03979747 0.2515778
## 183 183 9.777688 0.1840650 7.346410 0.3700630 0.03380819 0.1615531
## 184 184 9.766282 0.1862794 7.345501 0.5071169 0.03526456 0.2143516
## 185 185 9.780800 0.1839241 7.352517 0.4936978 0.03959702 0.2503143
## 186 186 9.752263 0.1877879 7.347666 0.4452894 0.02246241 0.2136088
## 187 187 9.847164 0.1724129 7.403973 0.3851670 0.04779406 0.2233413
## 188 188 9.770739 0.1855674 7.353068 0.4994980 0.03537189 0.2517242
## 189 189 9.777217 0.1844820 7.350929 0.5064168 0.03807318 0.2397773
## 190 190 9.767873 0.1860549 7.348075 0.5071745 0.03633485 0.2160583
## 191 191 9.777901 0.1843631 7.351659 0.5053529 0.03813373 0.2386879
## 192 192 9.710990 0.1955954 7.296361 0.4679568 0.01223436 0.1773079
## 193 193 9.710467 0.1956765 7.295535 0.4681224 0.01227607 0.1769849
## 194 194 9.710846 0.1956195 7.296352 0.4672094 0.01214289 0.1765839
## 195 195 9.903584 0.1630927 7.455669 0.4313776 0.05401281 0.2223542
## 196 196 9.747137 0.1889412 7.338040 0.4740632 0.02278413 0.2254485
## 197 197 9.747994 0.1887816 7.339549 0.4752755 0.02340342 0.2289336
## 198 198 9.748421 0.1887136 7.339830 0.4750986 0.02342800 0.2295458
## 199 199 9.711763 0.1954646 7.297599 0.4679643 0.01212524 0.1783861
## 200 200 9.712089 0.1954114 7.297899 0.4680368 0.01209371 0.1783917
## 201 201 9.711954 0.1954228 7.297856 0.4677251 0.01197920 0.1782884
## 202 202 9.843662 0.1733640 7.418321 0.5139677 0.04996301 0.3066963
## 203 203 9.776473 0.1849888 7.354496 0.5579042 0.02813249 0.2397958
## 204 204 9.712793 0.1952966 7.298579 0.4673249 0.01183193 0.1783530
## 205 205 9.846947 0.1729410 7.421109 0.5156754 0.05053357 0.3114863
## 206 206 9.768816 0.1858713 7.349420 0.5049857 0.03545023 0.2154665
## 207 207 9.712665 0.1953247 7.297094 0.4677898 0.01196921 0.1790613
## 208 208 9.777256 0.1848838 7.353368 0.5595925 0.02841093 0.2416870
## 209 209 9.758064 0.1868521 7.352071 0.4413222 0.02422457 0.2187009
## 210 210 9.830309 0.1750146 7.413086 0.4790664 0.04222900 0.2667830
## 211 211 9.713046 0.1952798 7.297714 0.4679258 0.01200062 0.1788622
## 212 212 9.713661 0.1951954 7.297866 0.4674915 0.01194017 0.1790801
## 213 213 9.772635 0.1853827 7.351436 0.5073761 0.03641022 0.2174050
## 214 214 9.713905 0.1951595 7.298138 0.4673039 0.01203417 0.1786011
## 215 215 9.785473 0.1834355 7.357869 0.5101646 0.03924981 0.2494564
## 216 216 9.714256 0.1951055 7.298302 0.4678542 0.01204842 0.1789006
## 217 217 9.786017 0.1829770 7.353938 0.3623824 0.03592279 0.1665485
## 218 218 9.714872 0.1950193 7.298600 0.4680072 0.01207305 0.1790553
## 219 219 9.715020 0.1949969 7.298801 0.4680128 0.01202056 0.1790669
## 220 220 9.715131 0.1949851 7.298787 0.4680137 0.01203149 0.1789404
## 221 221 9.751291 0.1883055 7.340550 0.4755239 0.02334139 0.2300752
## 222 222 9.715141 0.1949809 7.298526 0.4681280 0.01203892 0.1789291
## 223 223 9.715082 0.1949882 7.298287 0.4682542 0.01201889 0.1791110
## 224 224 9.751913 0.1881897 7.341525 0.4761998 0.02368617 0.2322449
## 225 225 9.778261 0.1845123 7.360318 0.5045028 0.03709413 0.2672089
## 226 226 9.777234 0.1850066 7.344146 0.5667707 0.03986442 0.2767922
## 227 227 9.788607 0.1830032 7.362579 0.4952423 0.04049777 0.2655269
## 228 228 9.789297 0.1837771 7.367967 0.6385308 0.04041038 0.3686853
## 229 229 9.775405 0.1852848 7.342174 0.5631779 0.03905983 0.2721519
## 230 230 9.790933 0.1824535 7.358134 0.3592697 0.03733926 0.1729544
## 231 231 9.777436 0.1846706 7.360030 0.5037751 0.03675608 0.2670504
## 232 232 9.714408 0.1950926 7.297743 0.4683593 0.01207440 0.1787876
## 233 233 9.786948 0.1833492 7.358447 0.5125386 0.03943818 0.2523509
## 234 234 9.851246 0.1727760 7.421434 0.5370260 0.05021810 0.3089969
## 235 235 9.985527 0.1508592 7.541721 0.5522606 0.06238269 0.3344816
## 236 236 9.769749 0.1858255 7.350410 0.5048567 0.03510150 0.2175733
## 237 237 9.776497 0.1851027 7.352050 0.5546727 0.02687995 0.2355181
## 238 238 9.790625 0.1825208 7.358714 0.3594360 0.03725063 0.1740700
## 239 239 9.957327 0.1547972 7.521318 0.5365630 0.05751046 0.3178205
## 240 240 9.714503 0.1950768 7.297804 0.4682653 0.01206096 0.1784811
## nvmax
## 19 19## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'## Coefficients of final model:
## (Intercept) x4 x7 x8 x9
## 8.941836e+01 -1.276249e-02 3.235631e+00 1.285802e-01 9.650356e-01
## x10 x11 x14 x16 x17
## 3.156375e-01 5.382116e+07 -2.523649e-01 2.760891e-01 4.401452e-01
## x21 stat13 stat14 stat24 stat60
## 3.914063e-02 -1.817820e-01 -2.758714e-01 -1.746312e-01 1.952430e-01
## stat98 stat110 stat144 stat149 sqrt.x18
## 9.490836e-01 -9.372953e-01 1.657180e-01 -2.076103e-01 7.619056e+00Test
if (algo.stepwise.caret == TRUE){
# test.model(model.stepwise, data.test, "Stepwise Selection", draw.limits = TRUE, regsubset = TRUE, id = id, formula = formula)
test.model(model.stepwise, data.test
,method = 'leapSeq',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,id = id
,draw.limits = TRUE)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 109.1 121.9 125.5 125.3 129.0 140.3
## [1] "leapSeq Test MSE: 90.3031382273639"
Stepwise Selection with CV (w/ filtered train)
Train
Test
LASSO (w/ full train)
Train
if(algo.LASSO == TRUE){
# Formatting data for GLM net
# you can use model.matrix as well -- model.matrix creates a design (or model) matrix,
# e.g., by expanding factors to a set of dummy variables (depending on the contrasts)
# and expanding interactions similarly.
x = as.matrix(data.train[,feature.names])
y = data.train[,label.names]
xtest = as.matrix(data.test[,feature.names])
ytest = data.test[,label.names]
grid=10^seq(10,-2, length =100)
set.seed(1)
model.LASSO=glmnet(x,y,alpha=1, lambda =grid)
cv.out=cv.glmnet(x,y,alpha=1) # alpha=1 performs LASSO
plot(cv.out)
bestlambda<-cv.out$lambda.min # Optimal penalty parameter. You can make this call visually.
print(coef(model.LASSO,s=bestlambda))
}Test
if(algo.LASSO == TRUE){
lasso.pred=predict (model.LASSO ,s=bestlambda ,newx=xtest)
testMSE_LASSO = mean((ytest-lasso.pred)^2)
print (paste("LASSO Test RMSE: ",testMSE_LASSO, sep=""))
plot(ytest,lasso.pred)
}LASSO (w/ filtered train)
Train
if(algo.LASSO == TRUE){
# Formatting data for GLM net
# you can use model.matrix as well -- model.matrix creates a design (or model) matrix,
# e.g., by expanding factors to a set of dummy variables (depending on the contrasts)
# and expanding interactions similarly.
x = as.matrix(data.train2[,feature.names])
y = data.train2[,label.names]
xtest = as.matrix(data.test[,feature.names])
ytest = data.test[,label.names]
grid=10^seq(10,-2, length =100)
set.seed(1)
model.LASSO=glmnet(x,y,alpha=1, lambda =grid)
cv.out=cv.glmnet(x,y,alpha=1) # alpha=1 performs LASSO
plot(cv.out)
bestlambda<-cv.out$lambda.min # Optimal penalty parameter. You can make this call visually.
print(coef(model.LASSO,s=bestlambda))
}Test
if(algo.LASSO == TRUE){
lasso.pred=predict (model.LASSO ,s=bestlambda ,newx=xtest)
testMSE_LASSO = mean((ytest-lasso.pred)^2)
print (paste("LASSO Test RMSE: ",testMSE_LASSO, sep=""))
plot(ytest,lasso.pred)
}LASSO with CV (w/ full train)
Train
if (algo.LASSO.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "glmnet"
,subopt = 'LASSO'
,feature.names = feature.names)
model.LASSO.caret = returned$model
}## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 1, lambda = 0.148 on full training set
## glmnet
##
## 6002 samples
## 240 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5402, 5401, 5402, 5401, 5402, 5402, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.01000000 9.689801 0.1979179 7.277215
## 0.01047616 9.688690 0.1980487 7.276272
## 0.01097499 9.687532 0.1981853 7.275287
## 0.01149757 9.686324 0.1983284 7.274247
## 0.01204504 9.685068 0.1984773 7.273167
## 0.01261857 9.683763 0.1986324 7.272054
## 0.01321941 9.682404 0.1987946 7.270905
## 0.01384886 9.680973 0.1989665 7.269696
## 0.01450829 9.679481 0.1991464 7.268431
## 0.01519911 9.677929 0.1993340 7.267118
## 0.01592283 9.676311 0.1995302 7.265759
## 0.01668101 9.674625 0.1997356 7.264342
## 0.01747528 9.672881 0.1999487 7.262873
## 0.01830738 9.671097 0.2001668 7.261366
## 0.01917910 9.669260 0.2003918 7.259797
## 0.02009233 9.667395 0.2006205 7.258188
## 0.02104904 9.665479 0.2008560 7.256524
## 0.02205131 9.663527 0.2010962 7.254819
## 0.02310130 9.661512 0.2013453 7.253039
## 0.02420128 9.659419 0.2016057 7.251175
## 0.02535364 9.657257 0.2018758 7.249250
## 0.02656088 9.655027 0.2021555 7.247263
## 0.02782559 9.652733 0.2024446 7.245235
## 0.02915053 9.650369 0.2027437 7.243159
## 0.03053856 9.647938 0.2030530 7.241061
## 0.03199267 9.645423 0.2033751 7.238941
## 0.03351603 9.642841 0.2037081 7.236781
## 0.03511192 9.640180 0.2040543 7.234569
## 0.03678380 9.637461 0.2044105 7.232338
## 0.03853529 9.634718 0.2047713 7.230168
## 0.04037017 9.631930 0.2051405 7.227992
## 0.04229243 9.629089 0.2055201 7.225762
## 0.04430621 9.626185 0.2059113 7.223498
## 0.04641589 9.623222 0.2063132 7.221213
## 0.04862602 9.620207 0.2067258 7.218868
## 0.05094138 9.617179 0.2071424 7.216601
## 0.05336699 9.614127 0.2075661 7.214336
## 0.05590810 9.611100 0.2079893 7.212172
## 0.05857021 9.608053 0.2084198 7.209995
## 0.06135907 9.604880 0.2088756 7.207749
## 0.06428073 9.601685 0.2093400 7.205441
## 0.06734151 9.598465 0.2098149 7.203179
## 0.07054802 9.595229 0.2102988 7.200873
## 0.07390722 9.591999 0.2107874 7.198442
## 0.07742637 9.588777 0.2112825 7.195949
## 0.08111308 9.585572 0.2117836 7.193380
## 0.08497534 9.582468 0.2122774 7.190859
## 0.08902151 9.579651 0.2127333 7.188483
## 0.09326033 9.576983 0.2131740 7.186204
## 0.09770100 9.574659 0.2135679 7.184236
## 0.10235310 9.572521 0.2139414 7.182450
## 0.10722672 9.570591 0.2142918 7.180810
## 0.11233240 9.568850 0.2146221 7.179397
## 0.11768120 9.567373 0.2149221 7.178367
## 0.12328467 9.566161 0.2151899 7.177624
## 0.12915497 9.565263 0.2154159 7.177096
## 0.13530478 9.564617 0.2156114 7.176793
## 0.14174742 9.564234 0.2157733 7.176687
## 0.14849683 9.564164 0.2158947 7.176774
## 0.15556761 9.564254 0.2160024 7.177079
## 0.16297508 9.564666 0.2160684 7.177707
## 0.17073526 9.565001 0.2161619 7.178535
## 0.17886495 9.565678 0.2162101 7.179783
## 0.18738174 9.566552 0.2162400 7.181423
## 0.19630407 9.567758 0.2162267 7.183404
## 0.20565123 9.569308 0.2161706 7.185855
## 0.21544347 9.571319 0.2160479 7.188739
## 0.22570197 9.573763 0.2158607 7.192074
## 0.23644894 9.576735 0.2155967 7.195930
## 0.24770764 9.580172 0.2152732 7.200229
## 0.25950242 9.584151 0.2148715 7.204952
## 0.27185882 9.588584 0.2144086 7.210283
## 0.28480359 9.593489 0.2138813 7.216049
## 0.29836472 9.598379 0.2133813 7.221806
## 0.31257158 9.603711 0.2128233 7.227954
## 0.32745492 9.609260 0.2122460 7.234263
## 0.34304693 9.615220 0.2116189 7.241105
## 0.35938137 9.621323 0.2109923 7.248157
## 0.37649358 9.627920 0.2103045 7.255659
## 0.39442061 9.634681 0.2096267 7.263357
## 0.41320124 9.642017 0.2088787 7.271615
## 0.43287613 9.649754 0.2081042 7.280190
## 0.45348785 9.658122 0.2072504 7.289317
## 0.47508102 9.666658 0.2064145 7.298674
## 0.49770236 9.675846 0.2055000 7.308639
## 0.52140083 9.685601 0.2045258 7.319131
## 0.54622772 9.696131 0.2034517 7.330297
## 0.57223677 9.706070 0.2025676 7.341064
## 0.59948425 9.716265 0.2017098 7.352028
## 0.62802914 9.725649 0.2011256 7.362719
## 0.65793322 9.735695 0.2005093 7.374050
## 0.68926121 9.746603 0.1998366 7.385976
## 0.72208090 9.758551 0.1990649 7.398880
## 0.75646333 9.771653 0.1981733 7.412773
## 0.79248290 9.786011 0.1971399 7.427560
## 0.83021757 9.801746 0.1959383 7.443450
## 0.86974900 9.818985 0.1945363 7.460476
## 0.91116276 9.837870 0.1928948 7.478637
## 0.95454846 9.858554 0.1909658 7.498074
## 1.00000000 9.881205 0.1886905 7.519044
##
## Tuning parameter 'alpha' was held constant at a value of 1
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.1484968.
## alpha lambda
## 59 1 0.1484968## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
Test
if (algo.LASSO.caret == TRUE){
test.model(model.LASSO.caret, data.test
,method = 'glmnet',subopt = "LASSO"
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 111.0 122.2 125.5 125.3 128.8 138.3
## [1] "glmnet LASSO Test MSE: 89.9613396773673"
LASSO with CV (w/ filtered train)
Train
if (algo.LASSO.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train2
,method = "glmnet"
,subopt = 'LASSO'
,feature.names = feature.names)
model.LASSO.caret = returned$model
}## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 1, lambda = 0.112 on full training set
## glmnet
##
## 5712 samples
## 240 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5140, 5140, 5141, 5142, 5141, 5142, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.01000000 7.495376 0.3032179 6.017033
## 0.01047616 7.494598 0.3033247 6.016488
## 0.01097499 7.493795 0.3034350 6.015936
## 0.01149757 7.492964 0.3035495 6.015360
## 0.01204504 7.492104 0.3036682 6.014755
## 0.01261857 7.491208 0.3037922 6.014112
## 0.01321941 7.490276 0.3039217 6.013439
## 0.01384886 7.489306 0.3040570 6.012735
## 0.01450829 7.488301 0.3041975 6.012002
## 0.01519911 7.487263 0.3043431 6.011262
## 0.01592283 7.486188 0.3044947 6.010511
## 0.01668101 7.485054 0.3046556 6.009712
## 0.01747528 7.483891 0.3048213 6.008917
## 0.01830738 7.482693 0.3049926 6.008105
## 0.01917910 7.481461 0.3051693 6.007268
## 0.02009233 7.480186 0.3053539 6.006410
## 0.02104904 7.478859 0.3055472 6.005507
## 0.02205131 7.477471 0.3057508 6.004560
## 0.02310130 7.476042 0.3059616 6.003582
## 0.02420128 7.474531 0.3061871 6.002531
## 0.02535364 7.472977 0.3064208 6.001445
## 0.02656088 7.471360 0.3066663 6.000290
## 0.02782559 7.469690 0.3069219 5.999090
## 0.02915053 7.467942 0.3071924 5.997820
## 0.03053856 7.466157 0.3074705 5.996494
## 0.03199267 7.464302 0.3077620 5.995118
## 0.03351603 7.462417 0.3080603 5.993743
## 0.03511192 7.460495 0.3083668 5.992344
## 0.03678380 7.458542 0.3086803 5.990896
## 0.03853529 7.456555 0.3090013 5.989427
## 0.04037017 7.454565 0.3093248 5.987968
## 0.04229243 7.452512 0.3096621 5.986468
## 0.04430621 7.450447 0.3100048 5.984988
## 0.04641589 7.448365 0.3103543 5.983535
## 0.04862602 7.446270 0.3107103 5.982100
## 0.05094138 7.444212 0.3110643 5.980757
## 0.05336699 7.442193 0.3114162 5.979510
## 0.05590810 7.440259 0.3117583 5.978357
## 0.05857021 7.438403 0.3120921 5.977263
## 0.06135907 7.436507 0.3124397 5.976128
## 0.06428073 7.434660 0.3127851 5.975117
## 0.06734151 7.432771 0.3131461 5.974056
## 0.07054802 7.431003 0.3134916 5.973001
## 0.07390722 7.429349 0.3138232 5.971926
## 0.07742637 7.427856 0.3141319 5.971009
## 0.08111308 7.426398 0.3144414 5.970143
## 0.08497534 7.425132 0.3147249 5.969384
## 0.08902151 7.424052 0.3149840 5.968749
## 0.09326033 7.423124 0.3152255 5.968160
## 0.09770100 7.422388 0.3154421 5.967650
## 0.10235310 7.421822 0.3156389 5.967285
## 0.10722672 7.421367 0.3158267 5.967133
## 0.11233240 7.421153 0.3159815 5.967016
## 0.11768120 7.421166 0.3161059 5.967026
## 0.12328467 7.421577 0.3161671 5.967393
## 0.12915497 7.422344 0.3161733 5.968139
## 0.13530478 7.423460 0.3161296 5.969251
## 0.14174742 7.424985 0.3160248 5.970699
## 0.14849683 7.426959 0.3158492 5.972637
## 0.15556761 7.429349 0.3156072 5.974963
## 0.16297508 7.432231 0.3152851 5.977672
## 0.17073526 7.435705 0.3148621 5.980737
## 0.17886495 7.439760 0.3143412 5.984225
## 0.18738174 7.444172 0.3137690 5.987994
## 0.19630407 7.448938 0.3131455 5.991898
## 0.20565123 7.453776 0.3125279 5.995958
## 0.21544347 7.459149 0.3118205 6.000428
## 0.22570197 7.464824 0.3110695 6.005179
## 0.23644894 7.470910 0.3102576 6.010256
## 0.24770764 7.477218 0.3094225 6.015633
## 0.25950242 7.484087 0.3084967 6.021495
## 0.27185882 7.491245 0.3075380 6.027682
## 0.28480359 7.499005 0.3064780 6.034375
## 0.29836472 7.506891 0.3054199 6.041075
## 0.31257158 7.515320 0.3042793 6.048175
## 0.32745492 7.523868 0.3031546 6.055575
## 0.34304693 7.532648 0.3020171 6.063226
## 0.35938137 7.541089 0.3009935 6.070619
## 0.37649358 7.550056 0.2999083 6.078383
## 0.39442061 7.559168 0.2988582 6.086252
## 0.41320124 7.569174 0.2976696 6.094762
## 0.43287613 7.580123 0.2963356 6.104071
## 0.45348785 7.592047 0.2948440 6.114199
## 0.47508102 7.605041 0.2931706 6.125449
## 0.49770236 7.619047 0.2913274 6.137403
## 0.52140083 7.633565 0.2894290 6.149636
## 0.54622772 7.648274 0.2875633 6.162288
## 0.57223677 7.661823 0.2860740 6.174261
## 0.59948425 7.676152 0.2844974 6.186892
## 0.62802914 7.690515 0.2830424 6.199805
## 0.65793322 7.705672 0.2815174 6.213444
## 0.68926121 7.720915 0.2801158 6.227100
## 0.72208090 7.736995 0.2786637 6.241277
## 0.75646333 7.753360 0.2773282 6.255863
## 0.79248290 7.771268 0.2757834 6.271433
## 0.83021757 7.790855 0.2739927 6.288138
## 0.86974900 7.812295 0.2719016 6.306271
## 0.91116276 7.835760 0.2694516 6.325996
## 0.95454846 7.861433 0.2665710 6.347355
## 1.00000000 7.889514 0.2631723 6.370364
##
## Tuning parameter 'alpha' was held constant at a value of 1
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were alpha = 1 and lambda = 0.1123324.
## alpha lambda
## 53 1 0.1123324## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
Test
if (algo.LASSO.caret == TRUE){
test.model(model.LASSO.caret, data.test
,method = 'glmnet',subopt = "LASSO"
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 108.6 120.9 124.2 124.1 127.6 136.7
## [1] "glmnet LASSO Test MSE: 90.9570476798876"
LARS with CV (w/ full train)
Train
if (algo.LARS.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train
,method = "lars"
,subopt = 'NULL'
,feature.names = feature.names)
model.LARS.caret = returned$model
}## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info =
## trainInfo, : There were missing values in resampled performance measures.## Aggregating results
## Selecting tuning parameters
## Fitting fraction = 0.414 on full training set
## Least Angle Regression
##
## 6002 samples
## 240 predictor
##
## Pre-processing: centered (240), scaled (240)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5402, 5401, 5402, 5401, 5402, 5402, ...
## Resampling results across tuning parameters:
##
## fraction RMSE Rsquared MAE
## 0.00000000 10.790951 NaN 8.228019
## 0.01010101 10.669060 0.1070230 8.138536
## 0.02020202 10.560541 0.1070230 8.060271
## 0.03030303 10.465810 0.1070230 7.991861
## 0.04040404 10.386326 0.1162167 7.934314
## 0.05050505 10.312043 0.1274646 7.879487
## 0.06060606 10.246557 0.1363653 7.829608
## 0.07070707 10.185586 0.1473175 7.780281
## 0.08080808 10.127085 0.1574593 7.732619
## 0.09090909 10.072015 0.1655614 7.687281
## 0.10101010 10.020612 0.1719111 7.643737
## 0.11111111 9.973306 0.1776243 7.602056
## 0.12121212 9.928466 0.1834298 7.562547
## 0.13131313 9.886562 0.1881846 7.524680
## 0.14141414 9.847636 0.1920539 7.488610
## 0.15151515 9.811724 0.1951848 7.454165
## 0.16161616 9.778858 0.1977034 7.421141
## 0.17171717 9.749093 0.1997137 7.389570
## 0.18181818 9.723498 0.2012598 7.360894
## 0.19191919 9.701326 0.2029834 7.336397
## 0.20202020 9.680750 0.2050612 7.314649
## 0.21212121 9.662600 0.2068439 7.294773
## 0.22222222 9.645988 0.2085230 7.276515
## 0.23232323 9.631498 0.2099801 7.260246
## 0.24242424 9.619427 0.2112130 7.246357
## 0.25252525 9.608629 0.2123226 7.233749
## 0.26262626 9.599441 0.2132789 7.223253
## 0.27272727 9.591521 0.2141265 7.214094
## 0.28282828 9.585056 0.2148156 7.206355
## 0.29292929 9.580052 0.2153049 7.200305
## 0.30303030 9.575822 0.2157248 7.195157
## 0.31313131 9.572714 0.2159946 7.191166
## 0.32323232 9.570335 0.2161657 7.187688
## 0.33333333 9.568603 0.2162471 7.184920
## 0.34343434 9.567291 0.2162808 7.182786
## 0.35353535 9.566363 0.2162641 7.181173
## 0.36363636 9.565693 0.2162224 7.179890
## 0.37373737 9.565134 0.2161761 7.178877
## 0.38383838 9.564881 0.2160882 7.178193
## 0.39393939 9.564542 0.2160292 7.177578
## 0.40404040 9.564349 0.2159567 7.177158
## 0.41414141 9.564308 0.2158683 7.176981
## 0.42424242 9.564362 0.2157729 7.176874
## 0.43434343 9.564487 0.2156753 7.176826
## 0.44444444 9.564859 0.2155427 7.176949
## 0.45454545 9.565384 0.2153894 7.177193
## 0.46464646 9.566064 0.2152178 7.177648
## 0.47474747 9.566832 0.2150378 7.178126
## 0.48484848 9.567861 0.2148213 7.178823
## 0.49494949 9.569020 0.2145895 7.179661
## 0.50505051 9.570252 0.2143518 7.180651
## 0.51515152 9.571568 0.2141081 7.181773
## 0.52525253 9.573034 0.2138456 7.183047
## 0.53535354 9.574594 0.2135740 7.184359
## 0.54545455 9.576245 0.2132935 7.185736
## 0.55555556 9.578021 0.2129975 7.187239
## 0.56565657 9.580040 0.2126663 7.188990
## 0.57575758 9.582209 0.2123155 7.190829
## 0.58585859 9.584503 0.2119495 7.192696
## 0.59595960 9.586966 0.2115619 7.194679
## 0.60606061 9.589419 0.2111816 7.196594
## 0.61616162 9.591955 0.2107939 7.198545
## 0.62626263 9.594559 0.2103995 7.200486
## 0.63636364 9.597217 0.2100002 7.202393
## 0.64646465 9.599855 0.2096089 7.204257
## 0.65656566 9.602485 0.2092233 7.206128
## 0.66666667 9.605158 0.2088353 7.208045
## 0.67676768 9.607850 0.2084492 7.209951
## 0.68686869 9.610514 0.2080724 7.211827
## 0.69696970 9.613190 0.2076977 7.213760
## 0.70707071 9.615976 0.2073099 7.215815
## 0.71717172 9.618831 0.2069156 7.217918
## 0.72727273 9.621711 0.2065213 7.220141
## 0.73737374 9.624653 0.2061209 7.222391
## 0.74747475 9.627606 0.2057218 7.224680
## 0.75757576 9.630587 0.2053222 7.227021
## 0.76767677 9.633590 0.2049235 7.229393
## 0.77777778 9.636651 0.2045198 7.231798
## 0.78787879 9.639791 0.2041080 7.234342
## 0.79797980 9.642950 0.2036973 7.236989
## 0.80808081 9.646134 0.2032879 7.239657
## 0.81818182 9.649347 0.2028776 7.242390
## 0.82828283 9.652601 0.2024652 7.245197
## 0.83838384 9.655887 0.2020513 7.248079
## 0.84848485 9.659210 0.2016352 7.251041
## 0.85858586 9.662568 0.2012179 7.254020
## 0.86868687 9.665983 0.2007963 7.257001
## 0.87878788 9.669488 0.2003657 7.260014
## 0.88888889 9.673129 0.1999189 7.263088
## 0.89898990 9.676840 0.1994659 7.266201
## 0.90909091 9.680535 0.1990190 7.269314
## 0.91919192 9.684212 0.1985789 7.272425
## 0.92929293 9.687921 0.1981387 7.275613
## 0.93939394 9.691633 0.1977021 7.278757
## 0.94949495 9.695338 0.1972702 7.281892
## 0.95959596 9.699087 0.1968357 7.285056
## 0.96969697 9.702870 0.1964002 7.288215
## 0.97979798 9.706697 0.1959624 7.291412
## 0.98989899 9.710592 0.1955188 7.294606
## 1.00000000 9.714503 0.1950768 7.297804
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was fraction = 0.4141414.
## fraction
## 42 0.4141414## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
Test
if (algo.LARS.caret == TRUE){
test.model(model.LARS.caret, data.test
,method = 'lars',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 111.0 122.2 125.5 125.3 128.8 138.3
## [1] "lars Test MSE: 89.9672610672758"
LARS with CV (w/ filtered train)
Train
if (algo.LARS.caret == TRUE){
set.seed(1)
returned = train.caret.glmselect(formula = formula
,data = data.train2
,method = "lars"
,subopt = 'NULL'
,feature.names = feature.names)
model.LARS.caret = returned$model
}## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info =
## trainInfo, : There were missing values in resampled performance measures.## Aggregating results
## Selecting tuning parameters
## Fitting fraction = 0.485 on full training set
## Least Angle Regression
##
## 5712 samples
## 240 predictor
##
## Pre-processing: centered (240), scaled (240)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 5140, 5140, 5141, 5142, 5141, 5142, ...
## Resampling results across tuning parameters:
##
## fraction RMSE Rsquared MAE
## 0.00000000 8.965132 NaN 7.151413
## 0.01010101 8.827399 0.1500471 7.053747
## 0.02020202 8.703557 0.1500471 6.967931
## 0.03030303 8.594207 0.1500471 6.891913
## 0.04040404 8.499253 0.1677379 6.825897
## 0.05050505 8.410441 0.1840918 6.765352
## 0.06060606 8.329136 0.1941970 6.709788
## 0.07070707 8.257852 0.2032007 6.660182
## 0.08080808 8.189768 0.2172935 6.609997
## 0.09090909 8.124849 0.2291276 6.560249
## 0.10101010 8.063873 0.2385402 6.511710
## 0.11111111 8.007761 0.2462789 6.466284
## 0.12121212 7.955037 0.2541572 6.423746
## 0.13131313 7.904846 0.2611683 6.383169
## 0.14141414 7.857920 0.2669333 6.344746
## 0.15151515 7.814319 0.2716456 6.308263
## 0.16161616 7.774099 0.2754747 6.274138
## 0.17171717 7.737422 0.2785792 6.242105
## 0.18181818 7.704929 0.2814914 6.213154
## 0.19191919 7.675310 0.2845708 6.186705
## 0.20202020 7.649490 0.2873692 6.164155
## 0.21212121 7.624930 0.2905413 6.143189
## 0.22222222 7.601360 0.2936384 6.123110
## 0.23232323 7.579593 0.2963706 6.104337
## 0.24242424 7.559883 0.2987312 6.087481
## 0.25252525 7.543125 0.3006710 6.073079
## 0.26262626 7.528196 0.3025591 6.060016
## 0.27272727 7.514239 0.3044106 6.047532
## 0.28282828 7.501918 0.3060651 6.037118
## 0.29292929 7.491020 0.3075476 6.027846
## 0.30303030 7.481449 0.3088360 6.019466
## 0.31313131 7.472751 0.3100092 6.011973
## 0.32323232 7.465200 0.3110163 6.005546
## 0.33333333 7.458341 0.3119253 5.999746
## 0.34343434 7.452279 0.3127138 5.994673
## 0.35353535 7.447045 0.3133879 5.990417
## 0.36363636 7.442159 0.3140237 5.986342
## 0.37373737 7.437813 0.3145819 5.982614
## 0.38383838 7.434105 0.3150420 5.979363
## 0.39393939 7.430926 0.3154256 5.976552
## 0.40404040 7.428485 0.3156833 5.974292
## 0.41414141 7.426361 0.3158976 5.972258
## 0.42424242 7.424590 0.3160577 5.970532
## 0.43434343 7.423274 0.3161473 5.969246
## 0.44444444 7.422246 0.3162008 5.968307
## 0.45454545 7.421503 0.3162121 5.967551
## 0.46464646 7.420982 0.3161934 5.967013
## 0.47474747 7.420822 0.3161152 5.966777
## 0.48484848 7.420724 0.3160340 5.966641
## 0.49494949 7.420895 0.3159102 5.966663
## 0.50505051 7.421113 0.3157855 5.966712
## 0.51515152 7.421497 0.3156383 5.966959
## 0.52525253 7.422013 0.3154732 5.967298
## 0.53535354 7.422586 0.3153051 5.967773
## 0.54545455 7.423301 0.3151182 5.968262
## 0.55555556 7.424173 0.3149097 5.968806
## 0.56565657 7.425156 0.3146853 5.969427
## 0.57575758 7.426238 0.3144477 5.970158
## 0.58585859 7.427403 0.3142008 5.970918
## 0.59595960 7.428630 0.3139469 5.971676
## 0.60606061 7.429975 0.3136749 5.972534
## 0.61616162 7.431382 0.3133963 5.973418
## 0.62626263 7.432867 0.3131082 5.974276
## 0.63636364 7.434408 0.3128147 5.975087
## 0.64646465 7.435956 0.3125247 5.975931
## 0.65656566 7.437512 0.3122389 5.976818
## 0.66666667 7.439067 0.3119570 5.977755
## 0.67676768 7.440734 0.3116591 5.978746
## 0.68686869 7.442460 0.3113550 5.979764
## 0.69696970 7.444286 0.3110378 5.980874
## 0.70707071 7.446209 0.3107081 5.982149
## 0.71717172 7.448159 0.3103782 5.983462
## 0.72727273 7.450196 0.3100363 5.984888
## 0.73737374 7.452278 0.3096915 5.986389
## 0.74747475 7.454392 0.3093449 5.987909
## 0.75757576 7.456512 0.3090009 5.989470
## 0.76767677 7.458642 0.3086582 5.991039
## 0.77777778 7.460808 0.3083119 5.992621
## 0.78787879 7.463023 0.3079598 5.994216
## 0.79797980 7.465269 0.3076060 5.995842
## 0.80808081 7.467559 0.3072485 5.997547
## 0.81818182 7.469820 0.3068999 5.999205
## 0.82828283 7.472083 0.3065548 6.000840
## 0.83838384 7.474333 0.3062160 6.002420
## 0.84848485 7.476582 0.3058819 6.003989
## 0.85858586 7.478831 0.3055518 6.005535
## 0.86868687 7.481077 0.3052262 6.007042
## 0.87878788 7.483320 0.3049054 6.008555
## 0.88888889 7.485632 0.3045765 6.010139
## 0.89898990 7.487956 0.3042490 6.011779
## 0.90909091 7.490310 0.3039200 6.013489
## 0.91919192 7.492682 0.3035915 6.015187
## 0.92929293 7.495099 0.3032591 6.016865
## 0.93939394 7.497567 0.3029220 6.018580
## 0.94949495 7.500104 0.3025771 6.020343
## 0.95959596 7.502697 0.3022261 6.022139
## 0.96969697 7.505342 0.3018694 6.023996
## 0.97979798 7.508020 0.3015108 6.025913
## 0.98989899 7.510757 0.3011470 6.027837
## 1.00000000 7.513584 0.3007718 6.029796
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was fraction = 0.4848485.
## fraction
## 49 0.4848485## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'
Test
if (algo.LARS.caret == TRUE){
test.model(model.LARS.caret, data.test
,method = 'lars',subopt = NULL
,formula = formula, feature.names = feature.names, label.names = label.names
,draw.limits = TRUE)
}## [1] "Summary of predicted values: "
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 108.6 120.9 124.2 124.1 127.6 136.7
## [1] "lars Test MSE: 90.9710422668425"